I've shot and recovered 2 deer with "memorable" results. The first was a buck shot with my .50 cal muzzle loader. The shot was in the front of the chest and totally exploded the heart (verified during the butchering process). When the black powder smoke cleared, he was gone and I was worried but just after the powder smoke cleared, I heard him crash in the leaves about 30 yds from where he was standing when I shot.
The 2nd was a button buck at about 80 yds. I shot him using 230 gr Sierra game king boattail spitzers (federal premium loads). He flipped over backwards and didn't move for a couple minutes as I watched. He was shot almost broadside through both lungs. As I was gathering my stuff to leave the blind and go to the deer, he jumped up and started to run. Piled up stone dead about 20 yds from where he was shot.
The point is sometimes their adrenaline will propel them even though they are actually 'dead on their feet'.