Stan, "using Remington Gun Club shells." I know you have had problems with B&P ammo. Completely agree to switch shells first. A problem moving from one side to another is unusual and most likely has only one cause as Keith says. Bad factory ammo is much more common than ever and promo ammo seems to be the worst. Right now they can sell anything that goes into a box, and it seems that quality control is lacking. I have seen some re-loaders seat a primer so deeply that it could cause light primer strikes. Again a ammo issue not a gun issue so much. It might have a issue with a little dried oil on the firing pins having gummed up things with a little crud. Good cleaning should cure that.

From a mechanical perspective, for a problem to go from one side to both side you need something in common for both to share. Hence the inquiry about loose screws. Do the firing pins protrude when the hammers are dropped? Do both move back and forwards like they are not gummed up? Start with a thorough examination, good cleaning, change of ammo and retest it to see if the problems still occurs. Nothing is more frustrating than an intermittent problem but your sounds like it is a persistent problem which should be easier to find. When ever I have a failure to fire, I go down the same checklist. Ammo, loading properly, action clean, action operation properly, close inspection of mechanics. Change only one thing at a time to see what the problem is. Ammo first because it is expendable and easiest. Are the primers seated flat to the base of the shells and are the primer strikes light? Sometimes a light strike can be confirmed by just trying the shell in the other barrel and have it work. Then go back and figure out why the first light primer strike like crud in the action. Try the ten dollar cure with new ammo and go from there after a good cleaning. Hammerguns are too much fun not to use.