I hate to sound like a broken record but, there is something outside the board causing the problem.
I have a remote that won't work. In working with Lippert (it's under warranty but was told to call them by the dealer) trying to determine the problem I got involved with the control board - I believe it is probably the one that you are dealing with. There are a few different models but they all have outputs to the various mechanical "things" (slides/stabilizers etc) if I recall. I would imagine they could unwire the outputs from the board and re-connect them one at a time and see if there is a slide or something causing a large draw thru the board that burns it out. Below are the directions I was given to find the info on the remotes and boards;
"You can also go to our website:
WWW.LCI1.COM and click on customer service at the top of page. Scroll down to ELECTRONICS and from there you will find all we have on our wireless remote systems. Under Lip Sheets (drop down menu) you will find all trouble shooting info and Manuals under the Manual drop down menu."
I have a TT, not a 5th wheel, and my board is located on the forward wall of the trailer in the pass thru compartment. It is just a black plastic box the, when removed, has all the wiring and the board. It is just above the batteries inside the trailer.
Don't know if it will help but at least it will kind of give you an idea of what might be going on and possibly give you some info to pass to the service manager at the dealership. Having put 5 different boards in, the service dept. is barking up the wrong tree. There are different kinds of boards and maybe a different kind would be beneficial? Good luck.