Ya, you probably have a capacitor that is wearing out. Sometimes they will arc internally and short out and the only way to stop it is to cut the power which causes the charge to drain out of them.
It's probably temperature related as to why it happens exactly when it does. You could set it out in the sun for few hours and I'll bet it acts up a lot worse then normal. In the shop they'd stick it in a low oven for while, but kids, don't try that at home.
Finding the actual bad component will be next to impossible without popping the cover and checking voltages while the thing is acting up. For that you'd need a scematic diagram which you aren't likely to find for any radio built in our lifetime.
Edit: If the radio has sentimental value or something you might be able to find a little shop that will be able to fix it for less then buying a new one would cost. But not much less.
[ June 23, 2004, 18:56: Message edited by: geoschmo ]