I once bow shot a buck at around 35 yards. It was a broadside shot thru the lungs. I sat in the stand for perhaps 10 minutes before the need to go see the spot where he was standing got the best of me.
Huge spray of blood from the shot. I figured he couldn't go far so in spite of knowing better I took up the trail expecting to find him dead in short order. The trail was one a blind man could follow with copious blood on the ground. I found where he fell 2 or 4 times with loads of blood on ground each time.
Honestly I thought all the blood he had was on the ground already. But he kept going. I kept following the blood even after it became just a drop on a leaf here and another 10 yards ahead.
Even now all these years later I still don't know what happened to that deer. My best guess is someone else found him and got him out. I lost the trail over a quarter mile from where I shot him. With so much blood on the ground I find it hard to believe he was still on his feet. Blood evidence told me the shot was in the lungs which I already knew.
If that deer was still on its feet where I found that last drop of blood it sure could operate with darn little blood.
A deer shot thru heart or lungs can run easily 100 yards on sheet will to live. Even if blood isn't flowing to the brain they can go that far. Beyond that I sure don't know how they do it.
That deer was double lunged and yet I lost the blood trail over a quarter mile from where I hit him with a blood trail that looked as if someone was throwing out buckets of blood. I have no explanation for such a thing. Perhaps your buck falls into that same category, maybe there just is no explanation.