You made the right call. Now if he'd had a gut wound or arrow sticking out of his neck, something that was going to eventually be fatal or cause him a lot of issues, I'd have shot him and I'm sure you would have as well.
2010 Hoyt Turbohawk (29", 62#)
29" Easton Axis N-Fused
100 Gr. NAP Nitrons/Slick Trick Standard
2010 200 Point Club (230")
2012 Largest shed contest winner
If he's eating and scent checking does, his senses are fine and he should make it. Good luck going for him next year!
Bear Charge 62#/29"
Kantpinch bear fur finger tab
Trophy Ridge Punisher 3-pin sight
Whisker Biscuit rest
LimbSaver Bow String Decelerator
Saunders Hyper Glide
Easton Raider Carbon Arrows
100gr G5 Montec