How could a skyhook stay in orbit with no human involvement for thousands of years
In the story I'm writing, three humans with stone-age technology and no knowledge of space accidentally awaken thousands of cryogenically preserved humans.
These humans immediately get to work on reaching space due to the presence of an AI gone insane from existential dread on the planet they are on. They will use large numbers of spaceplanes and multiple skyhooks to reach infrastructure designed for interstellar travel.
The problem is that these humans have been cryogenically preserved for thousands of years, meaning that the skyhooks would have to have maintained their orbit for all of that time without any human involvement.
Thankfully, advanced AI and nanotechnology exist in this story, and such things might help in keeping the skyhooks up. My question is how would they do it, and how might nanobot swarms and super AI help with this if they needed at all.
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They can "swim"
If they're "dragging" in atmo, and they have some power source (solar would be fairly trivial), perhaps they can have some sort of propulsion system that leverages that for stationkeeping, i.e. suck in the air that's slowing them down in the first place and exhaust it in an advantageous manner. Best case, they have air screws (okay, maybe jet engines) in advantageous locations. Worst case they're built something like a Bussard ramjet. (An ion drive might work, also.)
They are self-maintaining
You have AI and nanotech. Maybe the skyhooks are built with fabrication capabilities and have a fleet of AI-operated service craft to take care of them, including AI-directed mining of either the planet surface or space-borne resources (whichever is easier). The fleet of service craft can collect more fuel / raw materials as needed.
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