When a P22 won't fire, the first thing you check is the safety...flipped forward, lever parallel with the barrel is fire. If good to go there make sure a round is fully seating and the slide is closing and that there is a round in the chamber. If good to go there, unload, cock the hammer and make sure the firing pin is fully resetting to the rear and that it moves freely. If good to go there check the brass to see if you are getting a solid firing pin mark. It takes 8 lbs of pull to cock the hammer with a new main spring. Once is drops below 7 lbs hits become inconsistent. Some might fire, some not. Time for a new spring. Also if the chamber gets dirty and a round doesn't fully seat you can get a light stroke on the first hammer fall but no ignition. The problem is that the round "gives" with the first hit, is now fully seated and will fire with the second hammer strike. The problem here is a dirty chamber. Clean it. A round should easily drop into the chamber under the pull of gravity. But, .22s also get chambers dirty...so, a clean chamber always ranks up there with routine maintenance.
Rounds fully seating? Safety set to fire? Are you getting a firing pin mark on the rim? If not or if the strike is light time to check the other stuff. 1917