What kind of shape was he in when you recovered him? It is truly amazing how much drive a mature whitetail buck has to live. I have seen a buck with a arrow through one lung and an obliterated liver run for over a mile and a half. It has a lot do do with the scenario. For example if you live in an area with lots of predators the buck might be reluctant to bed down knowing he is injured and not wanting to be overcome by coyotes. Or if he is outside of his comfort area, he might try extra hard to get back home. It sounds to me like a slight quartering to shot. Which probably was a one lung liver shot.