A friend of mine had something similar happen one time. He shot a buck, I think with a muzzleloader, from about 80 yards out. It dropped like a stone and being a dufus...he either set his gun down and walked out to it or didn't reload. By the time he got up to it, it jumped up and staggered around a little and sprinted off! (I know at least one person was with him that day that watched all of this transpire and laughed hysterically. Unfortunately, I was not with him that day and could only share in the hilarity later, when the story was told to me.
At any rate, as best as could be figured...the deer was hit high, over the actual spine...but probably still on the "spinous process". (Which is the vertically oriented bone structure of the spinal column.) The shock of the hit dropped the animal due to a temporary shock to the spinal cord, but since the actual cord was not ruptured, etc, the beast recovered in the 2 minutes or so that it took him to get over to it and then ran off...apparently to live on.
Lol, I have a buddy that was hunting muzzy season with his dad 10-15 years ago and his dad shot a buck and dropped it in its tracks.
They walked up to it and while looking it over noticed it was still breathing but figured it was on its last breath. They set their stuff down, tagged it and started walking back to get the truck.
When they got back to the buck with the truck the buck was on its feet and walking away tagged and all. His dad tried getting back to the gun for a follow up shot but didn't make it before the buck made it back into timber.
They went after him but never seen him again. Never found a drop of blood either. Thought maybe he hit him in the base of the rack and knocked him out lol.