Need more info from OP to diagnose problem.
The rounds that did not fire, did you check to see if they were clearly struck by the firing pin?
What ammo were you using? Have you tried other ammo?
Did you have other types of failure such as failure to eject or failure to feed?
For the record, my wife and son both own a 597. We don't use Rem ammo with them, too many duds. Federal Auto Match and CCI ammo function 100%. Give those a try.