If you tell me it's never happened to you then I'm telling you its not if, it's when. So there's that.
There are many things that can help make the determination. A few years ago I stuck a monster bull in the leg. He ran off like nothing happened. I tried pursuing briefly but quickly realized I'd never see that bull again and went back to hunting. That stung and I would of loved to kill that 350+ bull. But I had to put it behind me just as fast as that encounter took place or risk not seeing another elk for the rest of that hunt. It would have ruined the hunt.
What determines when you throw in the towel?
Dad was on a blood trail more than 50 years ago with a buddy last day of Dec season. Tracked him all day til they ran out of light. Came back with the game warden next day to find the buck, dead in his bed. Only wound they could find was a cut foot pad. The bowhunter was able to sneak up on the bedded buck in the snow thought he hit it in the body cavity, confirmed it was the foot only after field dressing and getting it home for processing.
So if you have strength and sign left, I suggest don't stop. Might just be a short distance away...just don't know until you find them.
As you said, if you hunt long enough, odds are it’s bound to happen. You just have to learn from any mistakes and do your best to make sure it doesn’t happen again.
The other bull I lost, I videotaped (in 2014). He ran straight up a creek, and I never picked up his trail coming out. I looked for two long days, never found him. I didn't get complete penetration, but still thought there was a good chance he would die. Did tons of sweeps, grid searches, looked for birds, listened for bees, tried to smell him...nothing!
I tracked that one a couple hundred yards through the Pine duff without turning up a drop of blood and called it good.
But if I had a body cavity hit.... I figure there’s about a 48-hour window; either you’ll find it dead or you won’t, but if it’s dead, it’s spoiled and if it’s not, it will survive long enough that your chances of recovering an edible carcass are about nil.
That said, if you have sign, you’re not done yet.
Some years ago, my brother hit a cow high double-lung and she pinned him down where he didn’t dare risk a second shot. He was sure she’d tip over at any moment, but she eventually walked off with the herd. His arrow was well-coated with blood, but all the bleeding was internal. He’s a school teacher and can only hunt weekends, so he searched for a day and a half - including taking the dogs up the hill with him - and went back to hunting the following weekend.
2nd most Important thing is to make a good faith effort, exhaust your leads and make a serious effort to come up with new leads after you run out.
1st Most Important Thing is to take close, sure shots in the first place....