Pushing a poorly hit deer is the best way to insure it will not be recovered.
I have to agree with this 100%. The hardest deer for me to find was one that tried to jump my arrow after it nicked a small twig. It nicked the deer on the underside of it. After getting my arrow and checking the area of the deers movement I back away from it.
It was a wet rainy day and that only added to the missery of trying to locate it. I left it for an hour and a half as it was early in the morning that the shot was made. I also notices the white hair on the ground as well as a fatty substance on my arrow. Both which indicated a low shot or perhaps a gut shot. So I went home and let it lay for a while and got out my rain gear. It was a pain to track as it went up a ridge rather than heading towards a small stream as I would suspect. I was taught early in hunting that a wounded deer will walk with it's toes spread for balance and that played a big part in the recovery of it. I circled around for about 4 hours before I came acrossed it. While making my circles I noticed where a deer walked with it's toes spread up onto a ridge and sure enough when I got there it had gotten up and went down towards a cedar swamp. I knew right then with all the time that had elasped that I needed to go in behind it. It had laid down shortly after getting in the swamp. Upon seeing me it got back up only to recieve another shot this time connecting directly to both lungs and that was pretty much the end of it.
Upon the original shot it was hit only in the flank just under the belly area. The skin was still holding together and the penetration was roughly one inch going straight threw. So is it possible to recover with your shot? Based on my own experience I would say yes.. If not pressured in any way and given time to lay and bleed out I see no reason as to why not..