Just to clarify My JENSEN model JCD2006 in my OFF-ROAD POPUP is a stand alone regular AM/FM CAR RADIO type not a built-in model with a whole bunch of other things like DVDs sound system etc... I know this is nothing like what you are dealing with radio wise. Probably a big difference if it is part of a whole integrated entertainment system... My main comment was about how my F150 integrated VIDEO Screen and SOUND operated when being used. Thought it might have some reference to your problems with your sound dropping out.
Inside photo showing Jensen Radio and inside stereo speakers under the wrap around seating..

Outside photo showing the external mounted stereo speakers

My JENSON operated this way works fine for me... The ANTENNA is a simple rubber flexable whip type antenna mounted on the rear side of the popup main box area..

The only problem I had with mine was the way it was original wired in with just both 12VDC lead and ignition wire 12VDC wired together. I separated them and added a Radio Shack Push Button slide switch to the side of the radio install which acts like the key ignition switch in a car/truck install and now I just leave the main JENSEN ON/OFF ON all the time and turn the radio ON and OFF by using the slide switch. This allows me to keep all of my PRESETs in tact.

Of course if I store for awhile I will go ahead and shut down the whole the whole radio to keep from adding to the trailer parasitic power drains.