Radio power mystery

[68 ReNay]

sometime back my radio started to turn off and back on randomly when i'd rev the motor. i've had the radio in several years without problem. then recently, doing the same activity it would turn off and not come back on - every time i did it. id start the truck and the radio is on and working fine. tap the accelerator and it went out.

i'm not an electrician but i check to see that steady power was running through the wire, from the fuse block to the plug in the back of the radio. all checks out fine (even when the radio has cut off, i pulled the plug and tested it - the pen light comes on). there doesn't seem to be a short anywhere.

it's the strangest thing and i'm hoping someone knows whats up. i don't know that it matters but: '68, 350/350, original fuse block, kenwood CD player. . .

thanks in advance for any help you can offer!