I've had similar problems several times, with different cars and different radios. In every case it has NOT been the radio that's at fault. It has always been associated with the car's electrical system. The radio initially works fine for a short period but then the voltage supplied to it drops below a level where it can operate properly.
If you're lucky, you'll find that it's simply a slipping fan belt, resulting in the alternator not charging the battery properly. However it's often a symptom of a defective alternator, which is no longer doing the job properly. (I had one radio which exhibited this problem frequently from the first day on which it was fitted. After the car eventually broke down, requiring a new alternator, I never had the problem again. Two other car radios started exhibiting similar problems shortly before the vehicles' alternators packed up).
Chris