Is she spayed? If not, don't drop her off somewhere, it would be totally irresponsible. If she is spayed, assume she is at more risk for getting an infection from fights with other cats (if you were to set her loose somewhere), than of dying. Cats are survivors.
It's interesting that the vet can't find anything wrong with the cat ... I would have thought she had a disease or an infection, for her to be behaving like that. Do you have other cats? Is she feeling crowded? Has something big in her life changed?