Beaubeau -
My camper is in the shop right now for a very similar problem. The tech has diagnosed the problem as a bad thermostat and it is waiting for a replacement from Dometic.
My symptoms are: the AC (comp and fan) will run until the setpoint of the thermostat is satisfied and then cycles off. But it will never cycle back on even though the temp in the camper goes higher. I usually run it in AU mode and the step-down through the LO fan speed happens as it should at +4 degrees. I think if I have it in the LO mode, only the compressor is affected. The only way I can get mine to cycle back on is to turn the thermostat to the OFF setting, wait a few seconds, then turn it back on to any one of the AC settings (LO, HI or AU).
Like I said, the repair tech thinks it is a bad thermostat, BUT - I don't know if he is aware of the reset that Chris Bryant described. The tech never mentioned that and I don't think he tried it. So, when you try Chris' suggestion, please post the results here - I may need to get this info back to my tech.
Thanx