Other than fuel, what factors limit the lifetime of a spacecraft? For example, if someone wanted to send a spacecraft on a 100 year trip round the solar system and back to Earth, could it be done using today's technology, ignoring the orbital mechanics and merely focussing on power management and other similar issues?
Over how many administrations, regimes, revolutions, wars, etc. will a 100-year spacecraft operations need to be funded? If you expect to get data back, you will need to keep antennas and/or photon buckets (for laser comm) pointed at the thing, and you have to maintain and likely replace those assets over time. You are unlikely to design something completely autonomous over a 100-year time span, so you will also need to maintain a team to command the spacecraft. Whatever the science is, you'll need someone to point the instruments and say what data to collect when. You will likely need to navigate the spacecraft, and maintain a team for orbit determination and maneuver generation. If it is a sample return, then you will need to pay for someone to find the thing, pick it up, and conduct the science on the returned samples. 100 years later.
Many perfectly good spacecraft have been shut down due to lack of money. The threats to do so in the future continue.
There are probably a bunch of problems, but lets start with some easy ones:
Each side of the vehicle will differ in temperature a great deal, since one side will be in sunlight, the other in shade. You can do a rotisserie roll, as Apollo did on the way to the moon, but that makes maintaining lock on earth with an antenna harder.
Regardless, whatever materials the vehicle is made out of will expand and contract, a lot due to wide swings in temperatures and this will generate wear and tear.
Circuit boards do not take well to this as welds and solder can crack.
Electronics without adequate shielding will get overwhelmed by the high energy protons or beta radiation that will naturally be encountered.
Regardless of how good the shielding is, over a 100 year time frame, it is likely some damage will occur.
Solar panels degrade over time, so whatever power source you chose, must survive the 100 year time span which is currently unlikely.
Whatever is used for station keeping/orbit correction, will eventually run out.
Power System Duration
There is no more fundamental need on a spacecraft than a source of power. Except for some of the earliest satellites, spacecraft are fundamentally electronic systems.
While the radio-thermal generator is a long duration device, their primary failure point is the corrosion of the thermocouples. The 470We output of the Voyager probe is now significantly reduced - it should, based upon the fuel decay, still be around 350We... but it's under 300 watts at present. Many earlier generation probes have ceased function due to RTG thermocouple corrosion.
Solar panels also degrade over time, tho' how fast is a combination of other factors. Still, when the solar fails, the satellite is dead.
A full nuclear reactor is one of the most compact and powerful sources of electricity for spacecraft. It has the issues of the thermal to electric conversion systems, not dissimilar to those of RTGs, of corrosion and radiation damage, plus the limit of fuel. Once the fuel is used, it's used. Further, the fuel decays whether or not it is used; for uranium-233, 234, 235, 238, the decay is trivial, but can itself cause damage to other systems.
Several sources of mechanical wear are important. The most important is the thermal cycling - as an object heats, it expands (with a few exceptions, like water below 4°C), and as it cools, contracts. This can cause flexion and brittleness, and even cracking of components. The sources of this include operation of instruments, received sunlight, and venting of operational fluids (intentional or not).
Most spacecraft are in motion. This means also that they are likely to encounter other objects in the local space environment. Impact with such objects is a primary cause of failures of solar panels, and can cause failures of a variety of sensors as well. It's also both quite predictable for low level events (like solar wind damage), and quite unpredictable for high energy events (what people might term "impacts").
Operational vibration can be generated by instrument operational cycling, motors to move instruments, and minor impacts. As with thermal expansion, this results in flexion damage of the same kinds. It's also noted for loosening connectors if they are not properly designed; most space agencies account for this.
Friction wear is any wear caused by part A moving over part B. It's usually predictable, but is also a source of heating, and thus the mechanical wear of thermal expansion. Most friction wear is predictable for spacecraft; for landers/rovers, it's less so, due to environmental variables.
Radiation has multiple effects on spacecraft.
Radiation can directly set values in solid-state electronics; the smaller the microcircuitry, the more impact this has. This effect is usually not significant in terms of long-term lifespan, but can result in sudden terminations due to altered code. It's also routinely shielded against.
Radiation on materials, especially alpha and beta versus metals, can result in isotopic changes and/or fission (even of normally "non-fissionable" materials); over time, this can progressively result in changes in conductivity, brittleness, and tensile strength. These changes are particularly slow, but are part of the considerations needed for RTGs and Nuclear Reactors.
Radiation can also do direct damage to circuitry by removing bits of circuit (particulate), or by overloading circuitry (EMF and electron radiation).These can be shielded against, and are generally predictable, but subject to variations.
The largest issue with radiation is that spacecraft carry multiple radiation sources - antennae, RTGs and/or nuclear reactors - and must be designed to account for both onboard and offboard sources.
Not all materials used are long-term stable. Some are chosen for their very reactivity - this is true of reagents in chemical experiments, and of fuels - and others for specific properties during the expected operational lifespan.
Examples of reactivity by choice include hydrazine for thrusters, and the many chemistry experiments on various martian landers.
Examples of specific desired properties include gasket materials on fuel systems - the gaskets are a weak point and decay over time, but are stable enough for their expected durations. The gaskets used on the NASA SRB's are a different material than the gaskets on, say, a set of compressed gas valves, or on an ISS airlock door.
A Hundred Year Mission?
Radio-thermal generators probably could be designed that would be useful that long - provided the thermocouples can be replaced in flight.
Useful drive systems are going to be extremely limited, due to both fuel leakage and the inherent problems of limited delta-V.
Mechanical wear of that duration is a problem - modern materials have not been adequately tested for such durations, and semi-modern materials seldom have the durability for this type of duration.
A dead-fall target probe could easily pull off a 100 year mission - that is, a probe that simply is a target for spotting, and lacks active requirements - barring impacts, but as durations increase, impacts become considerably more likely.
And, likewise, the Pioneer 10 and 11 missions are still considered to be operating, even tho the probes themselves are unable to respond due to low power (suspected to be mostly from corrosion losses in the thermocouples); a small part of their mission was to be dummy targets. They are able to be found with extant telescope technology, and thus their position tracked, allowing for continuation of their mission. Their active mission phases, however, ended in the 1990's.
Mark Adler makes a good case for this being a matter of financing, but like always, there's two sides to the coin. If we put it in analogy, if we built a jukebox that could play for a hundred years, we'd also need someone to keep feeding it dimes. If it was really as durable, you'd get as much music out of it, as you'd throw money in it. But you also get one hundred years of amortizing your initial investment, and that's a lot of dimes. And that's the other part of the coin. If we could agree to listen to its music for one hundred years, it would make whoever built it rich. Going away from the analogy, rich in our case meaning lots and lots of valuable science done with a single space probe.
So in economic sense, this should clearly be desirable. In political sense, well we get tired of one single tune rather fast (read: there will be other politicians signing bills for it), so the device should cater for many different tastes. Meaning, there should be some incentive, a political motivation for it that would excuse its financing for a century. That's likely tougher to do than building it to last that long. But assuming we could do that, and opt to amortize huge initial costs of building and launching the spacecraft in a hundred years time, we'd get invaluable science out of it, and all the spin-off technologies developed for it a lot sooner than that even.
Of course, assuming it would work for that long. And that on its own wouldn't be an easy feat. As you make distance away from the Sun, renewable energy sources become scarce and infeasible (solar irradiance reduces with an inverse square to the distance from the source), so you'd have to pack a supply of power that would last. For the first leg of the journey, solar panels could be used while the solar radiative energy incident is still high, but eventually you'd have to rely on stored energy sources, say, RTGs. At that point, you start producing excess heat, be it by battery discharge, radioisotope decay, and so on.
Some of this heat could be used to heat the spacecraft itself and keep all its equipment within the thermal envelope it was designed for. And the solar panels could now double as excess heat radiators, but you already have one more consumable on top of propellants, and you're now producing local heat pockets that can't be easily dealt with by spinning the space probe like before in the inner Solar system due to proximity to external sources of radiation (your greatest worry now comes from within), so now all the spacecraft is a subject to wear and tear due to thermal expansion, and not merely its moving parts (which you might use less frequently to reduce damage through operation, but that option isn't really available for thermal expansion).
Could these problems be dealt with? Probably, but assuring a one hundred year long operation is a tall order and it would either require advances in material science we're not yet privy to, or the space probe would have to be built with redundancy in mind, one that could switch from a failed component to a working one, while keeping the rest of the standby units operational even though they're exposed to the same unforgiving environment. We could build a space probe with redundancy in mind today too, without major breakthroughs in material science (and other fields), but it would be heavy, difficult to launch, it would consume even more of its own propellants, take longer to get to places of interests (i.e. what we usually refer to as the tyranny of the rocket equation), be even more complex with increased chance of its individual parts failing (e.g. a good example are RAID disk arrays that, while their operational lifetime might be extended due to redundancy, have shorter life expectancy per unit simply for sharing the same enclosure and thus producing more heat), and perhaps more importantly, it would essentially be many space probes stuffed into a single one, with no advantage over simply launching many in various directions, each with expected operation of 10-20 years. And if something unpredictable happens with one or a few of them, others were at a safe distance and somewhere else during the incident.
And this brings me to the point I wanted to make. That even though there would be tremendous challenges, we likely could do it, but for the investment, you could simply have multiple, simpler and less durable space probes that could be more specialized for the targets they'd study, instead of having one that would outlast them all, but carry one hundred years old science equipment onboard. There just isn't any benefit to a space probe lasting for a hundred years. So this is what in my opinion is the ultimate limit of a space probe's lifetime. Our own patience with it.
In addition to Geoffc's answer, let me give a few others.
Intra solar travel is far more predictable and less harsh than low earth orbit, so we have the materials and technology to make something survive 100 years. The problem is chemical decomposition of the electrical power systems, primarily the solar arrays and batteries. Obviously we need backup components. But backups cannot solve the problem of chemical degradation that takes place before the backups are deployed. Therefore, the limiting factor is how fast the electrical power components degrade when they are not in use.
All other problems are solvable considering the problems engineers have already faced keeping the International Space Station aloft for 15 years and counting.
Thermal considerations: solved through testing and analysis. Consider the fact that the thermal environment on the International Space Station is far more complicated than an unmanned intra solar probe because it cycles in and out of sunlight once every 90 minutes. The ISS also endures days of direct radiation at a high orbital angles. Human living quarters necessitate thermal shielding much more protective than would be required to shield inorganic equipment inside of an unmanned probe. Large habitable modules are grouped closely with other large pieces of equipment and cast shadows over mechanical joints and other systems, contributing to the complexity. Our probe would be orders of magnitude smaller, and require much less analysis to cover all thermal cases due to the relatively static thermal environment.
Mechanical considerations: solved through testing and analysis. The lifetime of the mechanical equipment shouldn't be measured by time in service. There is a reason we measure an automobile's value based on the number of miles traveled and not age, and that 'highway miles' are considered less distressing than 'city miles'. The same concept applies to space travel; intra solar travel represents 'highway miles', planetary orbit 'city miles'. A mechanical joint might have a requirement of "degrees turned" or "open/close" cycles required. These numbers would be known in advance, especially for a piece of equipment meant to glide inertly across the solar system for years on end. The ISS has many rotary joints, two of which have been traveling ~360 degrees every 90 minutes for the last several years. Basically, we have the technology to create mechanisms with a service life of 100 years.
Other Environment solved through analysis: avoid asteroid belts and you'll probably be ok. There is a degree of uncertainty about whether the probe would be struck by an asteroid or degrade from space debris, but my guess is the debris flux in interplanetary space is much lower than in the low earth orbit currently occupied by the ISS.
We can build an object that will last 100 years drifting through empty space. This seems like a long time on the human scale, but is nothing in terms of the well-understood materials used in spacecraft. The big question is what we ask the probe to do.
Yes. It's a question of feasibility more than possibility. Solar panels degrade, batters decrease their depth of discharge, reaction wheels need momentum burns, but all of these things just state the requirement for bigger/higher start of life performance. For example, if we need 5W of power from the solar panels at end of life and we know the panels degrade by 1% each year they will be operating at (1-0.01)^100 = 0.634 * original power output by the end of life. So to find the start of life power required we can simply do 5W/0.634 = 7.88W. Therefore we need appropriately sized solar panels to give 7.88W. None of these numbers are really appropriate though, the degradation may be much higher and the power requires are likely to be much higher also.
Mechanical failure is a different matter. The typical way to deal with this would be to calculate the likelihood of failure and provide sufficient redundancy so that the likelihood is below an acceptable threshold. This will increase the mass and physical size of the spacecraft.
To sum up it's perfectly possible to build a spacecraft for a period of 100 years. However the feasibility of such a large spacecraft is unlikely to be favourable.
One final point, with some overwhelmingly precise orbit mechanics you could set a spacecraft on a trajectory that would give it a tour of the solar system and bring it crashing back into Earth. This spacecraft need not be operational at any point of this journey or the subsequent crash. This does fulfil your requirements though.
Voyager 1 and 2 have both been operational for 36 years; I believe they're our longest-lasting space missions to date. They're still in good working order. Their radiothermal power generators will probably give out in another ten years or so, but I don't see any fundamental reason that a Voyager-like probe couldn't be built with a 100-year lifetime. More/bigger RTGs would last longer, but entail adding weight to the craft, which would have to be paid for by reducing sensor payload or using a bigger launcher.