I started having a similar issue with my POD XT Live where the output would randomly become thin/trebley/slightly distorted for a few seconds and then return to normal. I found that the issue was rather simple. On the rear of the pedal next to the input jack, there is a "Norm/Pad" switch. The contacts on this switch were dirty, and it was randomly making contact while I was playing. I sprayed contact cleaner into the switch and switched it back and forth a number of times, and this fixed the output issue.
Since this is an old unit, I decided to clean all the potentiometers, input/output jacks, and switches with contact cleaner.
Hope this helps out someone else with this issue!