Does it happen when the car is stationary? Does it happen with the engine off? Do you have any problems with other circuits in the car that are fed off the accessories power e.g. cigarette lighter, power windows etc?
If it only happens to the radio with the engine on and more when you are driving it sounds like there is a loose connection or dry soldered joint in the power supply for the radio or in the radio.
You might have to connect a test lamp or DMM (digital Multimeter -Voltmeter function) to the power feed where it goes into the radio itself (or as close to the radio as you can get) to prove whether the problem is with the power into the radio or it is in the radio itself, i.e. either the power is on all the time at the radio power input point or it comes and goes.
If it is with the feed to the radio you need to check the wiring path from the radio fuse in the fuse block right through to the radio itself.
It may be for instance a loose connection at the rear of the fuse in the fuse block.
What type of fuse is installed? If it is a knife blade type check that the female connection point in the fuse block looks OK and that it has enough tension on the fuse. If it is a glass type fuse, again is it tight in the fuse holder, have you tried a different fuse of the same rating?