The combination of too much headspace and not pulling the trigger properly can do just what's happening. Normally, not pulling the trigger completely to the rear will just cause inconsistent pin strikes and accuracy will suffer. Fixing the headspace issue will require a new barrel.
Mine had too much headspace, so I flat filed the back of the barrel before fitting it to a frame, H&R won't do that, I'm sure. If the headspace is in their spec, they might put a slightly longer firing pin in it, dunno. It could also have a weak hammer spring which wouldn't be the first reported here. I bought some extras from Numrich, Fred has one or two of em as he had problems too.
Tim