If it goes to the amp parameters page that indicates a knob has moved. Knob jitter is always a culprit. Set all your Pod knobs to "0" except master volume and then change patches. Sometimes a knob will move just slightly and change a parameter, which sounds like it may be your volume or drive knob.
Actually, run every knob up to 100% and back to 0 a couple times, then set them all except master volume to 0 and then change patches and see if that cures the issue. Good luck!
I neglected to mention to do that on your amp as well. As it's probably an amp knob moving. Not enough coffee today, sorry. Set all amp knobs to 0 except master volume and reverb if you use your amp reverb instead of Pod. That should eliminate knob jitter.
I have a weird situation. I'll be playing my JTV-69 through L6Link to HD500X through L6Link to DT25 112 and after an random amount of time the HD500X will switch to the amp parameter edit screen and the amp will go silent. All pieces are still operating, and if you change the HD500X to another bank the sound comes back.