Re: Radio Going on and off
I would find the fuse for the radio and check that its a tight secure fit.
Also test it for continuity, and any concerns, just change it.
I don't think it's your battery, cause if it was weak or damaged enough to turn off the radio, I seriously doubt it would turn the car over to start. But for peace of mind, it never hurts to load test the battery periodically.
Auto Zone or Advanced will do it for free.
You might also want to yank the radio at some point, and check the power wires/harness, and ground connections, for a secure tight fit...