If you don't SEE it fall or HEAR it fall, give it an hour before you trail. If you saw and know that you hit it back, more than 4-5 inches behind the elbow, let it go for a few hours or more. Way back.. let it go for nearer 6-8 hours or overnight.
As long as the deer is alive, it won't spoil, even in hot temps so if you leave it 8 hours and it dies after 7, then it has only been sittung dead for an hour.
Many, maybe most deer will either run fast and die running, or will run to the nearest safe cover.. say 80 yards away or so, and stop and watch their back trail. If they feel they are not being trailed they will bed nearby and that is where you will find them if allowed to die.
ChuckC