If checking all the lines doesn't work, I still recommend the relay:
The symptom you list is the exact same one I have. I'm still planning to isolate my mute line (my parrot is feeding both my head unit and empeg, currently in parallel).
As the car warms up (on trips > 1-2 hours), some sort of low level current or noise charge builds up, and I get pauses when more current is being pulled from the car's system (depressing voltage) such as: opening/closing windows, turning on compressor, hitting brakes, etc. all activate the mute until I stop pulling that current.
Over time (next hour), it just gets stuck permanatly on mute until I pull the empeg...then the headunit unmutes, and I can still use radio/CDs.
I've got the additions to my harness all put together, but I haven't bothered pulling it all out in the months since I put it together.
Seriously though: isolate the empeg's mute line with a relay, I bet it'd work...
-brendan