Sounds like you have that footswitch assigned to Amp1 Bypass. Look in Setup > MIDI/Remote > Bypass.
Thanks for your help, Rex! I think I found the issue and have edited my post above to reflect the solution:
EDIT 2: I may have found the issue. Somehow, 'Smart Bypass' was enabled for this switch in default Layout 4. None of the other Amp1 channel switches had this enabled. I disabled it and all seems well again.