Let's suppose that an advanced alien civilization explored the Earth hundreds of thousands of years ago and then left a satellite in a high orbit, say of a radius of 100.000 km.
Could such a satellite survive for that very long time, so that present–day space explorers might find and retrieve it...?
Certainly. For instance, the two LAGEOS satellites, orbiting at 5,900 km, are expected to remain in orbit for eight million years or more. Those satellites were made especially dense, which will also tend to slow orbital decay. But less compact satellites in high orbits should do fine for long periods as well.
Yes. Look at the moon round the earth, asteroids around the sun, comets, and many other natural objects.
A satellite is "just another object". If they can have orbits that last billions of years, it's fairly certain an appropriate object created by humans and placed in an appropriate orbit, could last a very long time indeed as well.
The limitations relate to the mass and size of the object, and any friction or other effects it experiences. So all things being equal, a tiny satellite in the same orbit as the moon, would last a long long time, but it might be more affected by microimpacts, solar wind, heating/cooling effects, gas emissions (the moon has had a long time to stabilise but our satellite may still release tiny amounts of vapour/gas for many years as it warms/cools), low level gases in space, etc. It also lacks the sheer mass and momentum/angular momentum to absorb potential tiny causes of drift.
So it might not last as long, but it would seem likely to have the potential to last a very long time indeed, if not necessarily billions of years. How long? That depends on size, design, orbit, object orbited, etc. I'd be amazed if it wasn't of the order of >= millions of years with comparative ease, but that's a guess, not informed knowledge.
