I've had my Kemper since July and it has been absolutely stable. Today I ran into some variant of the "sudden no sound" problem. A reboot cleared it. The problem has not reappeared. This thread is - from my perspective - for documentation only.
I had just imported five profiles from the exchange (AndrewC's Carr Rambler profiles; very nice, BTW!) and was auditioning them in Browse mode via the Last Imported view. I was not rapidly changing profiles, unlike other similar reports. I was using the <> buttons to change profiles; I played at least a few notes on each profile, so they couldn't have been changed any more frequently than once every few seconds. On one visit (not the first) to the fifth of five imported profiles, sound stopped and the tuner appeared. Switching to Tuner mode then back to Browse removed the tuner display, but didn't restore the sound. IIRC, the first four of the five just-imported profiles still had sound, but the fifth didn't; other profiles in other views also didn't have sound. Nothing appeared amiss given a cursory review of settings and indicators.
I didn't think to grab a backup specifically for purposes of reporting this issue, and deleted several of my own profiles before capturing a fresh backup. I have that backup and a backup from before today's import if that'd be useful.
BTW: this is firmware 2.1.1 8823.