If I had to bet on one predator I'd go with the Great Horned Owl. When you say, "but does not eat it" are you saying the animal is complete in a pile there just gutted and headless??? The guts and head are laying there with the rest of the body???? If not, then the predator is eating something...predators just don't kill for the thrill of it. Is there usually a pretty good sized tree over where you find the possums??? Not necessarily huge tree but good sized with at least a fairly horizontal branch???
I know that for certain, a Great Horned Owl will really decimate the raccoon population by eating the kitten coons when they first start to leave the den with their mother. Owls kill possum too, but they usually wait until they are about half grown because they ride on their mother until they are too big to do that.
Edit: if it is an owl, you might be able to find it's roost...they like big long leaf pines. You will see what looks like splashes of white paint on the ground under the roost tree. If you look closely you will find "pellets" which are the undigestables that the owl spits out later...hair and bones mostly. If you find the roost you can tell for sure cause you will see the possum fur in the pellets.