Remington ammo has been plagued with problems for the last couple years, dunno if the primers are to blame, but I'd blame them if the rifle has plenty of pin protrusion and the pin strikes are nice and deep, I've had a LOT of rem 9½ primers fail to fire. It could also be a combination of issues starting with a chamber that's cut slightly too deep allowing too much headspace, when a round is in the chamber, is it flush with the barrel face, or slightly recessed? If it's recessed, that in combination with any barrel to frame gap can lead to no fires, it's not uncommon and needs to be addressed by H&R.
Tim