The MMRTG uses Pu-238, which has a half-life of 87.7 years. So after 14[1] years it should be able to output a little over 80% of the power, which naively to me seems like it should be enough.
What is the limiting factor of the MMRTG? Is it just an engineering decision?
Obviously other parts of the rover probably won't last 14 years, such as perhaps the batteries or wheels, but that is a separate issue.
14 years is the design lifetime for the MMRTGs. The thermocouples do degrade over time while exposed to the high temperatures of the hot side and the temperature changes of the cold side. The output power of the RTGs drops over time by degradation, design lifetime ends when power generation drops below the specified minimum level.
But many RTGs did work better than conservative lifetime calculations:
From Radioisotope Power Systems Reference Book for Mission Designers and Planners by NASA and JPL. JPL Publication 15-6
Thermal stress may cause little cracks in the material, this will increase the internal resistance of the thermocouples and thus decrease their efficiency and reliability.
There are also atomic effects degrading the thermocouples:
Thermocouple performance may degrade over time due to precipitation of dopants in the material, sublimation of the thermocouple material, or changes in thermal conductivity of unicouple alloys. The output power degradation due to thermocouple degradation is ~0.8% per year, depending on the material and the operating conditions. Radioactive decay of the Pu-238 causes additional degradation at ~0.8% per year.
(From page 5 of the handbook)
The Pu-238 decays exponentially 0.7868 % per year, so the degradation of the thermocouples should be exponentially too. 1.6 % during 14 years, that are 20.21 %.
($ 100 - 1.6 \% = 98.4 \% $ ; $ 0.984^{14} = 0.798 $ ; $ (1-0.798) * 100 = 20.21 \%$)
So they may have selected 20 % power loss over design lifetime and got 14 years as a result.
The 20 % are confirmed by the GPHS-RTG, the predecessor of the MMRTG.
Table 17 of the reference book.
285 W at the begin of mission BOM and 227 W at the end of design lifetime EODL are a drop to 80 %. 1.6 % degradation per year and 14 years, the same as MMRTG.
A plot of the power degradation. 0.8 % per year for the Pu-238 decay alone, 1.6 % for both the degradation of thermocouples and Pu-238.
To get a higher voltage many thermocouples are connected in series. If one thermocuple of the column or one of the connections fails, the whole column will fail. If there is only one column, the whole RTG will fail. If there are several columns in parallel connection, the output current and power will be reduced.
If all works well many RTGs of the past have worked much longer than their design lifetime. We should be happy if they work longer, but there is no one to blame if an RTG fails when reaching 115 % of its design lifetime.
RTGs are not fueled just before launch but about 3 years before. So degrading starts long before launch. RTGs are expected to perform during these 17 years.
This is an addendum to @Uwe's answer. RTG lifetime is a topic of much discussion in the planetary science community, and in particular the MMRTG being currently the only available RTG. MMRTGs decay much faster than GPHS-RTGs (see my comment to Uwe's answer), with an output power half-life of a bit over 16 years, the result of both Pu decay and unicouple degradation. The usual schedule for RTG production, testing, and integration into the spacecraft indeed has launch about 3 years after fueling, but NASA does have an "accelerated schedule" process with only 2 years between fueling and launch. That would put the stated lifetime at about one half-life of the RTG after fueling.
That is a problem for some mission concepts aimed at Uranus or Neptune, especially Neptune. Arriving at Neptune with a V-infinity low enough that it doesn't outrun current chemical propulsion system capabilities means a fairly long transfer trajectory, 13 years or more. If you used MMRTGs for electric power you'd have to launch with almost double the power capacity you'd need when you arrive at Neptune, and that uses a lot of extra Pu and project budget. Hence the current call for NASA to finish development and flight qualification of its planned "Next Generation RTG" ("NextGen RTG") in time to use the trajectories with Jupiter gravity assists to get to Neptune. I have a technology paper submitted to the British Royal Society that discusses this, and NASA's Outer Planets Assessment Group (One of the "AGs" that assesses and provides input to NASA's Planetary Science Advisory Committee about NASA science mission plans; I'm on its Steering Committee) is bringing that schedule concern to the attention of NASA.
If a Neptune mission used aerocapture instead of a chemical propulsive maneuver for orbit insertion, a long transfer trajectory isn't necessary. Saikia et al. (and in the paper behind that poster, unfortunately behind a paywall) concluded that the higher the V-infinity of approach, the better aerocapture performs, i.e. the smaller the uncertainties in the atmospheric exit state and thus in the final captured orbit. In that case, with gravity assists and Solar Electric Propulsion you could get to Neptune on what I call a BOOH trajectory (Bat Out Of ... uh, Hades), in as little as 8 years, and RTG lifetime would be much less of a concern. Of course, then you'd be throwing the problem over the wall to the Thermal Protection System (TPS) folks who must design an aeroshell with a TPS that will survive a 10-15 minute extreme hypersonic pass through a mostly-hydrogen atmosphere.
Indeed this question touches on a topic important to planetary exploration.
+n!
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