I do my best to recover the animal, as another has stated, a lot of times the animal survives and thrives. So unless i can physically see the animal and cannot physically recover it, then no I don't notch my tag.
I skinned out a bull elk that was breeding cows. Pulled a few year old arrow out fulling scar tissued up along his upper ribs. It was under the spine inside the chst cavity. Muzzy 125 on the tip. Tip was lodged in a vertebrae right inline with the front legs. It had broken off healed over and he was kicking ass that year.
I’m pretty good about showing enough restraint to not take questionable shots in the first place. Still though, I’ve made a mistake or two in my life on shots, and have made every effort to recover. That said, I don’t feel the need to place a self-imposed penalty on myself for a rare, and honest mistake. So yes, I would feel ok to continue hunting. I just thought this was something that for-profit TV hunters did. I really don’t know many people that would set fire to $1000 NR piece-of-paper tag. Folks don’t do that in real life do they?
If I make a good shot and can’t recover the animal despite my best effort, I consider it lost. That’s unfortunate, but on me. I’ll keep hunting only if I have another tag.
I have spent a couple of days tracking a wounded animal before. More than once I’ve gotten a 2nd shot and recovered the meat.
I will look all day and all day the next day. If I don’t find it I keep hunting. I’ve been lucky and never had to do this for an animal that I shot. I’ve recovered every single one within a couple hours. A friend of mine took a shot at a big old muley, saw him scrunch, found a blood trail. We looked for a day and a half before we went back to hunting. Pretty sure he just nicked a foreleg.
I saw a man do a very fine thing once. It was a hunter in an adjacent camp. He spotted a yearling mule deer buck who just had one little 2 inch spike. The little buck was badly wounded so the guy put him out of his misery and hung his tag on it. He was an accomplished hunter with many large four-point plus bucks under his belt. He did it because he did not want the Young Buck to suffer. Think I would do the same, but I’ve never been presented with this dilemma. I know it tears me up to think of them suffering.