Sounds like a bad solder connection. No need to use flux alone. Instead inspect all of your solder connections that are in the signal path of the channel that cuts out. One trick is to turn the chassis over, turn on the amp, and with headphones on and the volume set low, gently tap each solder connection with a chop stick. When you find the bad connection, you'll hear it make noise as you tap.
Reflow that solder connection using a little bit of fresh solder.