I just got another P32 in trade. I've carried a P32 for some time (rotating it with a LCP or G19, depending on situation). My old P32 has been reliable and I've had no issues...this one is a bit of a bear though.
I load CCI ball only, but have tried some HP rounds and a few Fiocchi rounds. All do the same, so I'm pretty sure it's not ammo related. I've tried 2 mags and same thing.
What happens is the first round would fire and then the pistol would lock up to the point where I'd have to drop the mag - using quite a bit of force to pull it out. The next round never chambers, but the slide goes forward and it appears it is ready to fire. Both magazines run fine in my other P32. I have no idea what generation this one is, but it looks brand new.
So, before I contact KT and ship it off, anyone here run into this issue before?

Try the KTOG, way more traffic and talk about Kel Tecs there than here.

try googling " P32 rim lock ", you can see some of the remedies, maybe,

I called Keltec, they took my details and shipped me a replacement magazine. I didn't really trust that fix,  but ran a few mags through it and sure enough, it ran like a champ.

2nd generation pistols have a large visible screw head which sits at the rear of the extractor; this is visible on the exterior of the slide. If it doesn't have the large visible screw head, it's a 1st generation pistol.