Not really; we deliberately set up satellites into their orbits such that they’ll broadly stay in orbit. The only way for an object to “escape” like this would be for gravity to just randomly stop functioning for brief periods, which doesn’t happen.
Satellites *do* have to take steps to remain in orbit, but the problem isn’t keeping up with Earth, but rather taking steps to ensure they don’t fall back to Earth as their orbits decay due to very very light interactions with Earth’s atmosphere.
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