Sounds like you're shooting bulk pack or Remington gold bullet/Thunderbolt ammo. But first, you should clean your rifle thoroughly as sometimes crud build's up around the chamber that causes misfires. But, the cheaper grades of ammo often have misfires or as we all call them "fail to fires" (FTF's) these days. Try rotating the round and firing again before discarding. Sometimes the primer compound is not evenly spread inside the rim. It could also just be a weak spring or dinged up firing pin. Could also just be junk ammo.
I never have much problem with standard velocity rounds killing small creatures. But for larger stuff, I would certainly use hollow points such as you were shooting when you started this thread. HV rounds such as CCI Mini-Mags are usually sufficient, but obviously Stingers and Velocitors probably work better.