The commander at Severnya states that the satellites are at 100km orbit. This is far too low to sustain a stable orbit. Satellites need at least 500km to be stabe for any length of time.
You can have a satellite orbit at any altitude. If it isn't affected by the atmosphere then all it needs to do is orbit faster. If it is then it'd need to be propelled, and as you see in the film it is and obviously moves about quite a bit so NERRR! :P
At just 100km altitude, a satellite will most definitely be affected by the last remnants of the atmosphere. It would be lucky to survive a couple of orbits before re-entering and burning up.
As for being propelled, satellites carry small thrusters for re-alignment, and perhaps a few minor altitude boosts, but it would be totally unfeasable for a satellite to carry enough propellent to sustain extended orbit within the upper atmospheric drag zone.
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