i was thinking broken wires and you posted this,im thinking we are thinking same general direction,had a galaxy 66v act like that,new wiring harness cured itI don't know if this will help but it is an experience I had with a brand new Icom 7100.
I bought for a bargain basement price and all the dealer told is it will cut out.
I got the radio hooked it up and started testing. I measured the power supply and it was set 13.9 Vdc. I keyed it up into a test load and it shut down almost immediately.
The only thing that I could see is the the wire feeding.the radio looked a bit small.
I hooked my DVM up to the wires right at the radio and the voltage dropped below 10.8 Vdc. That is where the radio shut down was set to protect the radio. I replaced all of the wire and reheaded the cable. I used heavier gauge wire and soldered the connectors and the wires for the fuses to the spade lugs. A couple of hours of soldering wire stripping and the radio was fixed. If you have a meter check the connector right on the back of the radio and see what your voltage does when you key up.