You don't need a stable orbit, just one that will keep it in our neighborhood and away from the atmosphere and congested orbits.

Put it in a high orbit, and point a telescope at it every now and then to update our record of it's orbit. By the time we are ready to visit it, even if its orbit changed, its new orbit would not be any more inconvenient then where we left it.

The moon's lumpy gravity field actually causes the eccentricity of most orbits to raise quite fast, eventually bringing the periapsis below the surface (or the apoapsis on an escape trajectory, but I recall the former being more of an issue): https://www.youtube.com/watch?v=EadClM4Y45A