The problem with the ISS is that it cannot simply be left in its current orbit, because there is a (miniscule) amount of atmospheric drag acting on the structure to continually slow it down. Since the first module was placed in orbit, we've had to periodically boost the ISS back up to its nominal orbit (e.g. using the space shuttle's RCS engines while it was docked, or the station's main engines on the Zvezda module) to compensate for the effects of drag. There are additional forces which perturb the orbit (irregular density of the Earth, solar wind, variations in atmospheric density and composition, etc.) but drag is by far the biggest factor.
If left alone, this drag force will eventually slow the ISS so much that it falls from orbit on its own, and we won't be able to control when and where that occurs. Something that massive falling from orbit poses a safety hazard, so by intentionally de-orbiting the station at a time and place of our choosing, we can control where it falls so that nobody is put at risk.
Now the considerations for saving the station:
- We would have to configure the station such that it can remain intact and safe if left unmanned and unmaintained for a long time
- We would have to move the station into a stable orbit that is out of the way of any other operational vehicles
The first point is actually more difficult than it first appears. The ISS is very heavily dependent upon its crew for repairs, and wouldn't be able to function for more than a few months without maintenance, so most, if not all systems would have to be shut down. You might be able to run some low-power, self-contained experiments on board, but that runs into the next problem:
The station is huge, but actually very delicate. Things like radio antennas and solar arrays would have to be stowed or removed, otherwise they could exacerbate the effects of getting hit by small debris. The solar arrays in particular can also contribute to undesirable rotation of the station (due to gravitational gradient and solar wind effects) which could ultimately damage the station. Without solar arrays, there is no power, and without power, there is no attitude control, monitoring or communications, and most importantly, no thermal control. The station would have to rely entirely on passive heating and cooling, which aren't the most stable things in orbit.
Finally, the station contains a lot of volatile materials such as coolant liquids, water, air, thruster gases, etc. Most of these would have to be vented from the station beforehand, because any leakage later on could act like a small thruster, causing the station to rotate or change orbit in an undesired way. Batteries and fuel cells would have to be removed or fully discharged to avoid undesirable (and potentially explosive) chemical reactions in the uncontrolled environment aboard the station.
Now to the second point: getting the thing out of the way. You actually don't have to go to interstellar space to preserve the station, as some other answerers have suggested; the Moon has been in stable orbit for millions of years and will happily remain so for millions to come. The question is: how far do you have to go to avoid bothering other satellites and rockets? The answer is a graveyard orbit, an orbit a few hundred to a few thousand kilometers above geostationary where old satellites go to die. Objects placed in such an orbit can theoretically stay there forever.
This is the bugaboo: because the ISS weighs a staggering 420 metric tons, it would require an enormous amount of propellant to move that bulk from 400km to 37,000km! (Think Saturn-V levels of propellant.) Nobody wants to pay for the rocket(s) and fuel to do that, or all of the preparatory work for Bullet 1 above.
So while I and many others would agree that we should preserve the ISS as a matter of World Heritage, unfortunately the cost to do so would be, quite literally, astronomical.
