You realize this is the 87-96 section? I know we're smarter than the guys driving the newer F150's and allot more experienced, so allow me to be the first to say Hello and Welcome to the Forums! Lol
That's a strange issue that you have going on. You need to get your self a fuse tap that you insert into the fuse slot for those outlets. Make yourself a jumper wire to plug into the fuse tap and get a multimeter and see if the power is being cut at the fuse. I can only imagine that there is some sort of protected circuit in there causing this. It just does not sound like a fuse issue. If it were the fuse itself, you would lose power completely.
1995 SWB 300 I6, M5OD, 273 gears, 235/75r15's, 21MPG, 50" Led Light Bar, 6" Off Road Lights, Full Synthetic Fluids, K&N RF1012
"Gentlemen, we can rebuild them. We have the technology. We have the capability to build the world's first unstoppable truck. The F-150 will be that truck. Better than it was before. Better, stronger, faster."