Ok, this makes me wonder, in the movie "Gravity", when people accidentially got separated from the space station, they were not forever lost?
Thus, in low earth orbit, at a speed of 8000 m/s, a relative speed of 8 mm/s is a fractional change of 1 in 1 million. The orbital period is 90 minutes, a millionth of which is half a second. That doesn't seem like much, but objects in orbit move really, really fast. Arriving at the same spot half a second later means you'll miss the other object by 4 kilometers! Without active guidance, a rendezvous in orbit is near impossible.
Only if going perfectly sideways, i.e. keeping the same distance from the center of the gravity well ("and the tolerances are inhumanly small").
Go down, you'll spiral to the bottom; go up, you'll float away, maybe to the Sun or Jupiter or just the Ooort cloud and beyond.
(I don't think you'll find another stable orbit without some sort of maneuvering jets or very well tossed bits of spare mass you may have on you. Even so your distance from the station is probably unrecoverable.)
Ultimately, to actually come back down to Earth you have to burn off a lot of sideways speed (especially if you don't want to be going too fast when you enter the atmosphere). And, to leave Earth's gravity, it takes quite a lot of acceleration too.
On the plus side all those weird interactions with real life allow you to do fun things like change orbit with electronic tethers or orbit around nothing by exploiting Lagrange points