10 to 12 hours at least, if I KNOW, or have very strong reason to suspect that it is gut shot.
Yes, if you wait that long and the deer has been dead a while before you find it, it may be spoiled, or the coyotes might get it, but at least you have a better chance of finding it because if you let them bed and don't push them they usually don't go that far. That, and most gut shots leave very little, if any, blood sign. So unless you have snow cover, you'd have to be almost psychic to be able to track one any distance. A gut shot is a FATAL shot. Not quick by any means, but fatal. That deer WILL DIE. Now it's up to you to determine how far it will go before it does. The less distance there is between where you hit the deer and where it first beds makes it easier for you to find it after it's dead, or hopefully sick enough that you can finsih it off. Not the best of scenes, but it does happen.
The WORST case scenario is to start tracking and puch the deer from it's bed. The usually go quite a ways then and the odds of you ever finding that deer again are very low.
Offer No Apologies.....
NRA Endowment Life Member