Mine did (does) the same thing, but I always have the Satellite radio on. Best guess would be a bad ground connection on the rear gate. There are two studs with a nut on each one in the upper outer corners. Try cleaning those connections up and see if it gets any better.
The antenna amplifier is located above the rear window under the interior trim piece, its a little aluminum box, with a coax connector running back to the audio stack and a pair of wires (antenna lead and ground?) one is black the other white, and the box itself has a small bolt holding it to the upper gate so technically it is also grounded to the tailgate. There is a second one in the left rear corner under the lower trim piece access door (where the amps are) near the floor for the AM/Diversity antenna on that side of the vehicle as well.
The rear window heater is grounded to connector C0382 which is on the upper tailgate at the bottom of the window glass on the right side under the inside trim. It is then grounded to the body at connector C-0555 which is inside of the right rear wheel well (the one closest to the back seat - there are two there C0555 and C0706).