I think an object can spiral away but not escape (not moving fast enough), so after spiraling away for awhile, it reverses and spirals toward. Either it's moving fast enough, or it's Skylab. Might take a few hundred thousand years ;-)
Hmm, maybe an object can only spiral away if it’s accelerating — i.e. gaining kinetic energy. Which would mean an unpowered object like a satellite or space station could only spiral inward, though perhaps losing altitude at a very slow rate. The presence of any drag at all, even from a few air molecules here and there, would keep the case of maintaining a fixed orbit from being possible. Does this geekery sound legit to you? :-)