It is probably a Camplifier shutdown.
You can check this by connecting the Monitor Out (line level, not speaker) to another monitor system or even plug in your headphones directly into the Monitor Output. Leave the Kone Mode on, even though it will sound weird.
Do the drop outs appear even without or before the Camplifier?
You were correct, No dropouts with another monitor system or direct to headphones. I can turn up the Monitor Volume/Kone Volume to the max and it won't shutdown. Add back the Camplifier and it shuts down. It can't handle the backing tracks, which I guess is suspected at 25 W. It's still a great product for guitar signals, or to power regular speakers or even the Kone/Kabinet but it won't handle music at higher bass frequencies. I think Ritter Amps' Camplifier SHP (140W per channel) would work. I've got an email into them, wondering if they've tried it. Also, as others have said, I think the Seymour Duncan 700 would work well too. Thanks for the reply's CKEMPER and others.
Update: Works perfectly with an older Crown Micro-tech 600, very loud . . . . . . too bad it weighs more than a small car.