Just to be clear, the problems I've encountered (both with a P-3AT and in the past - once - with a Colt Pony) have NOT been failures to fire - they've been extraction/ejection problems. The one time I experienced it with the Pony, it was with a Winchester Silvertip. The round fired, but the expended case failed to extract, and was left in the chamber. The next round from the mag was jammed up against it.
As for the P-3AT, I've had this happen on two occassions. In both cases the pistol had been loaded for at least 3-4 weeks without cycling (and by cycling, I don't mean complete replacement of the ammo - I just mean the chambered round being removed and replaced). Both times the round in the chamber fired fine, but the empty case failed to be fully extracted/ejected, and ended up jamming the pistol, sitting within the ejection port horizontally (as it were extracted, but not forcefully enough to fully eject it).
In neither case had the pistol gotten wet - and both happened during the summer, so cold wasn't an issue.
These are the ONLY two failures I ever had with that pistol, and I never had them again once I started ejecting/chambering a new round on a weekly basis.
It could be any number of things - the round could be somehow corroding and "sticking" to the chamber walls. I suspected something like this, as my carry round in the P-3AT is Fiocchi FMJ, which has a brass case (not nickled). However, the failed rounds didn't look tarnished or corroded in any way.
It could be that after sitting for a period of time, the lube was congealing and making the slide move slower on the first round, and that "exercising" it weekly resolved it. I find that unlikely, though, as I don't tend to overlube, and on the P-3AT I used only FP-10 oil. Slide action seemed very smooth.
Pocket lint has not been much of an issue - I blow the pistols off and find very little. Note that it's not my practice to carry a pistol for months at a time without preventative maintenance - but I did want to run this test to make sure if I did go a few weeks without babying it, that it would still be something I could rely on.
Just to be clear - I'm not slamming the P-3AT in any way. With proper treatment, I trust it will fire every time I need it to. I've replaced it with an R9s because I like the higher quality (which of course the R9 has, with its significantly higher price) and the more powerful caliber.