I have 2 Kel Tecs I hate to admit. They both function well with any kind of ammo. The P-11 I bought used, it's an older model. It took a lot of years to get it to function reliably. I would work on it, then shoot it, only to discover it its still a jam waiting to happen. It would sit for months, then I would come up with a new idea. Finally I got it running. Then the new model Kel Tecs came out.
The new model Kel Tecs had all the polish of the P-11 after I was done with it. I was down to a JA-22 for a pocket gun. I got a good deal on a P-3AT so I bought it. It was a nightmare! No matter what kind of ammo I fed it the P-3AT malfunctioned, so I sent it back to Kel Tec. When it came back it hung up on the very first shot I fired with it. The feed ramp was cut down to a tiny triangle. Just by the work on the feed ramp there was no way the P-3AT could function, so I sent the gun back to Kel Tec. When I got it back the barrel had been replaced and a lot of polishing had been done to the gun, especially on the front of the rails the slide runs on. The P-3AT actually worked with any kind of ammo.
From my experience Kel Tecs reliability issues are caused by failing to properly strain the finish coatings. The P-11 started running after I cut a board to fit under the rails and glued emery cloth to it. I used the sanding block to remove the gobs of debris from under the rail. From what I could see the P-3AT had the same issues.