I had a DVD/entertainment combo that did the same thing. It was a short in the sub woofer wire (after warranty replaced the unit three times I discovered this myself), so the diagnosis seems correct. Your radio is probably fine just doing what it was designed to do.
Can you disconnect wires from the backs of the speaker one at a time to find the bad one?
I do all my own stunts
03 Dolphin LX 6355, Workhorse W22, 8.1 vortec, 04 CR-V, Blue Ox, Brake Pro----Norm, Barb and
Doc(He's a PhD)