Radio sound goes off & on. 2000 Jimmy

Hi, I have a problem for the books! The radio speakers in my 2000 Jimmy Diamond Edition go off whenever they feal like it. It used to happen only in very cold weather, but now it happens often, in all weather. Sometimes, going around a corner or a bump makes them go back on for a while. I have had the radio out of the dash to check all connections. They are fine.
Here's the strange part. My wife disovered that if we use the right rear electric window control to lower the right rear window a little, and raise it back up, the speakers always come back on. Then, after a few minutes they go off again. Doing the window thing always works! It is not a problem with the power or ground wires of the radio because the lights and controls on the radio are lit up and are operating fine.
It's a factory installed Delco stereo with CD player.
Could it be a wire to the speaker in the right rear door? All the speakers go silent. Thanks, Tom