Hei. I have a 2009 1.6 Honda Civic and I hit this extremely wired problem.
If I drive the car for more than 30 min in the summer or 1 h in the winter time my radio goes berserk and keeps shutting on and off continuously. I am noticing that this happens after the motor gets warm or maybe to warm in the summer. If I use the warmer now, being that it is -10 celcius, at max power, after 1 h max it start's the berserk. In the summer 20 min are sufficient.
It's extremely frustrating and I have not found a similar problem here. Or maybe I have missed the thread. Any advice?

 

Did you or someone else install an aftermarket radio? Sounds like it's wired into a 12v power source that's not constant. Somehow hooked into the heat/AC system wiring. I'd have an electronics tech look at it to see if he can figure out how it's wired. I believe Bubba has been under your dash.
Duane

 

Or possibly the radio has an intermittent short inside and turns itself on and off with the change in the interior temperature in the vehicle. If that's the case, you need a new radio.
Duane