Replace the electronic sensor on the side of the transfer case. It is a little ring looking part that is inside the square box that actually changes your transfer case gears. My truck has done this off and on. Sometimes I'd be driving and it would go to auto 4x4 and sometimes 4hi. I've even had it say it was in neutral when I started truck. Cycling the key works for a quick fix but the part is only about $70 to fix it right. Don't change the dash switch out. As if you do you're wasting money. My uncle works as head mechanic for a local dealer and once I done mine it has been problem free.
the F-350 in my post above has the V-10 6.8L in it. It's a real turd on hills and it averages about 6-6.8mpg pulling the boat. We have about 25000 miles on the truck and 23,000 of them are towing that load.
Boat and trailer is about 9000 lbs. It's a 26' SeaArk with a 350 in it. We car an extra 30 hp motor on the back. It has an on board 7.3K generator. It really squats the poor little F350. I'm guesing there is about 3000 lbs tongue weight.
I know it's a ford pulling the boat guys but I didn't have a picture of my truck pulling the 2 rhino, 18' trailer, and my sportman touring in the back of the truck. I'll have to post it later.
This is what I pull daily at work.