I used to have a car radio which would cut out for several minutes shortly after starting the car before eventually switching back on. The fault had nothing to do with the radio. What was happening was that starting the car was draining the (elderly) battery sufficiently for the voltage to drop below the level t which the radio would operate. It took a while for the alternator (also elderly) to provide sufficient charge to bring the voltage up to the critical level.
If the problem with your radio is present even when the engine isn't running, you can ignore this post as your problem is obviously unrelated to mine. However, if your problem only occurs when the engine is running (especially if it's shortly after starting), I suggest getting the battery and alternator checked.
Chris