I had the opportunity to remove the bulkhead in my 3850RL basement to tighten down the water pump connections due to a slow leak. While in there, I started checking connections in general and found the Coax connections that I could see where all very loose, not even finger tight. I don't know that you can get to the TV antenna coax connection easily, other than climbing on the roof to see if the antenna one is exposed, and then the connection behind the on/off button for the amplifier, and finally the connection behind the TV. Of course there are probably a few splitters in the basement or in a wall somewhere if you have multiple TV outlets in your unit.
On my old bumper pull trailer, I had similar symptoms you note, and it ended up being a lose coax connection on the roof from the antenna.
2017 Cardinal 3850RL Mocha Pearl full body paint
2016 F350 Lariat 4x4 FX4 SRW CC SB 6.7 Magnetic Metallic