The lesson that has served me best in my (relatively short) time in the elk woods is an echo of what's already been said, if they are still on their feet and you can see them, KEEP SHOOTING.
My first bull i literally stumbled into, we both stared at each other dumbstruck when we bumped into each other. He spooked out to about 75 yards broadside and I was hiking, rifle over my shoulder. Quickly shouldered my rifle, no rest and let one rip. He was still on his feet, so I quickly racked another and steadied myself and sent #2. Turns out #1 was a complete miss but #2 did the trick and put him down. Barnes TSX 180 gr for what its worth.
Fast forward to a deer hunt last year, i lost a deer on opening weekend of 2nd rifle, absolute gut punch and a poor decision that I regret still. I wounded it but a combo of buck fever and misjudging my holdover led to a wound that I never recovered. Second weekend of the season I had a very comfortable shot on a buck, took my time, was solid, and watched him get very wobbly after about 10 yards but he was still in the open. 0 hesitation sent round #2. I lost some backstrap bc i was higher shooting down, but he dropped on the spot and I have 0 regrets.
I am firmly on the side of keep shooting. "But you'll lose more meat" would you rather lose 5 lb from shot #2 or 200 lb from potentially not recovering the animal?
Sounds like a lot of factors added up but the one that rung familiar to me was not getting the second shot out. Practice the quick follow up shots and always take them. sorry about the luck, best you can do is learn from it and improve for next season!