This is exactly why I have joined this site as well. My 2011 Fiesta with 100K+ miles on it began this behavior last year (@75K miles). After about an hour, the sound system began popping at regular 6 second intervals, turning the entire system off for 3-4 seconds. This will continue for as long as the car is operating (meaning an 8 hour drive is maddening). The strange additions for my radio include: 1) I discovered last summer that I could maintain the radio without the popping noise if I ran the volume above 17. This, for a while, alleviated the problem. Then, for an unknown reason, the bluetooth and usb audio inputs would not work at all. The SYNC would not work at all. I could listen to SIRIUS, a CD, or the Radio. This went on for a couple of months over the summer and then just as suddenly, I got into my car one day and saw the bluetooth light on. The SYNC worked, and the popping noise was not as prevalent.
This lasted until late Fall. Then it all started back up again. Popping starts at about 45 minutes. The increased volume will give me about 10 more on SIRIUS but not on radio, CD, or USB. THEN, the radio began its interpretation of a possessed item. It will increase its own volume very loudly, then the volume plummets to almost inaudible regardless of the stereo volume. This will last for anywhere from 5-20 minutes and then either return to normal volume with the popping sound or go back to extremely loud and also popping.
IT's maddening I have a one hour commute to work and it literally drives me crazy. Protip, this happens even if I DO NOT TURN ON THE RADIO! I can drive without the radio on and it starts popping after 45 minutes. Insanity. Looks like replacing it with something else is the only way to go but I don't know if I can exchange this built-in monstrosity. What puzzles me is, why is this problem continuing with additional model years? I also received the $800 bad news on replacing it and I also said no thank you. I'm not giving Ford $800 to fix a problem they should have addressed years ago. I also have to say, this problem, and looking at this thread the extensiveness of it, has led me to not want to buy a Ford ever again.