I have found gut shot deer alive as much as 24 hours after impact. They weren't in good shape but nevertheless alive. My experience has been a deer hit in one lung has a better chance of making it than a gut shot deer. Septic shock is a killer albeit a slow one.

Even when you have lost the trail keep looking in beding areas and you might find your deer. I have found them as much as a half mile away from where they were shot even though they were never pushed so don't beat yourself up to bad.

Your experience is further proof that even the real simple and most ethical shots can go awry. If a person has enough shot exposures sometime, somewhere, somehow, something will go wrong. I guess that is the way most things in life are.

Good luck, I wish you well.