Alex, you are not alone, in this matter. I had this same sound on several profiles, and it was unpredictable, as to when it would occur. I ended up sending it back to Kemper, and was told by my sales rep, that they couldn't really find the problem, but replaced the board in it anyway. So, over the past year, when is got it back, everything seemed fine, and so I took it out on a gig last week. Suddenly, one of my lead patches started doing this really loud clipping noise, just like before, and I had to stop using the patch, just to get through the gig properly. A hard strum brings this obnoxious noise out, and I cannot figure out what is causing it either.
Odd, a hard strum fixed the issue. Maybe you turned something off and you didn't figure?
Did you save the faulty rigs and tested it with the new KPA? Did you still have these ones?