You could make a jumper, from the B+ input to the amp, to the turn on input (unhook whatever you have going to the turn on now). Make is something easy to unhook, so you don't kill your battery. If this fixes the problem, then it is a turn on issue.

Dalton, I think he is saying that the amp turns off, making a thump, while the radio is still on. Not just a turn on thump, as your scenario would create.

Toby