It sounds like you fell into the trap of thinking that there is no gravity in Space. There is, everything near earth still falls down to earth, nothing just “drifts away”. So how do satellites stay up? By flying sideways so insanely fast that they are falling but are literally missing the earth. That’s what being in orbit means. We’re talking about kilometers per second fast here.
With that in mind: Drifting into space would be impossible for a satellite, as it would take a lot more energy (speed) to do so. As for falling back down, there is still a tiny bit of air drag that would get a satellite down eventually, but satellites have a small booster with some fuel that they use to boost back up. It doesn’t need much, so it can keep this up for years without a problem.
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