Someone else posting that it camped over there body. No idea of time limit. You should be able to draw it off though. It will only chase so far and then it should go back to its original location. Sleeping won't help as that doesn't seem to advance the rest of the game, just changes day/night cycle.

Best to go 3 stamina based foods so you can run more often. But don't let stamina go all to zero. You can walk for a bit and be alright if you have a decent lead from running.