I have an 02 dodge quad cab that my radio comes on then quits. It doesn't matter weather I'm using the cassette deck or the radio. The clock continues to work, the fuses have been changed. I even replaced the radio and the replacement does the same thing.

I believe it IS an intermittent power problem, While it is on and working pull fuse to verify that fuse, I would check power in and out of that fuse while inoperative to see if a fuse prior to that is losing it. Also verify you have a good ground.