I have the same issue. I have two DS4 and none of them is working well. Controllers disconnect every 10 seconds. I can't do anything, I can't play, I can't use the menu, nothing. I had this issue in my old house, I moved out and I have the same issue here, I moved the PS4 from one place to another, I tried to use it with a wire and without one...
I use it in horizontal position. I have Sony's smart tv Bravia, Sony's speakers and subwoofer, Sony'a PS3 and PS4. Everything's from Sony.
Don't know what else to do.