I shot a big doe one time at 10 yards that hopped once and started looking around like, "What happened?". Then she blew once, and continued to stand there. Then she started to get wobbly and fell over. She was 3 yards from my arrow in the dirt.
I had a friend shoot a buck at 39 yards that he said never moved after the hit. Double lunged him and he stood there for probably 10 seconds and then just fell over.
On both of these examples, upon examination during cleaning, no bone was hit on entry or exit. The arrows entered between two ribs and exited between ribs. I think the lack of "impact" had something to do with the deer's reaction.
Out of approximately 235 bow killed deer that I have the information on, these were the only two instances where the deer didn't seem to react to being shot.
So I say run and drop.