I've had problems with the similar system in our '10 31'. Several technicians checked things, and never fixed it. In desperation, I called Dometic, and talked with a nice, friendly, customer service rep type person who was no help. Finially asked for a supervisor to call me back, and then after explaining what all had been done with no success, he explained to me the whole system works as a computer, and is powered from the front AC unit (12 volts) over the small telephone four conductor (22 ga wire) with the little telephone clip-in connectors. The problem is, neither the wire or the connectors are of sufficent size to provide the needed 12 volt
DC amps to power and control the thermostate/computer. The symtom of the display going out on your thermostate is one of insufficent power to the unit.
My problem was a bad connection at one of the telephone connectors in a cuppling block under the inside cover of the front AC unit. Replaced it with a $7 piece from Radio Shack, and it has been working ever since.
Hope this is of some help.