Richard Smith wrote a book about recovering deer. He cited a study that quantified a percentage of deer harvested that showed some sign of previous injury. Of those past injuries attributed to hunting, a fairly high percentage were healed gut shots. So I will disagree that all gut shot deer die within a few days. Most probably do though.

Sounds like the arrow took a strange path through that deer. Entry wound where it should be, yet exit wound back and high. I would guess the diaphram is punctured, probably one lung hit to some degree, and obvioulsy some gut as well.

I'd track it as far as possible, then grid search. Always check sources of water with gut shots. Be ready to shoot if you see the deer again. It will probably be weakened and allow you to get fairly close.