Tad,
At one time I had a Duotherm Distributorship for mobile homes and as a small sideline we also sold roof airs. We would not do repairs. The issues were many...not the least being the poor quality of most RV roof air systems. Repairing them can be done by replacing relays and external parts but it usually is a one way deal. If the unit comes on and the compressor phases off after about 15 to 45 seconds, you have a leak in the system and with these, that is a big issue. It takes a dedicated person to repair a leak but it can be done but not always. Once the system has been violated, it is really troublesome. From what you have described, you have a relay of some sort that is failing periodically. Check your voltage meter for the 120 v's for starters as well. Again, from what you described, the encouraging thing is that the compressor does indeed come on for 15 to 30 minutes and then phases off. Recently on one of my units, the compressor would stay on after the fan had shut off. It was the control board itself ($300). It failed because of a low voltage into the coach at a RV park without proper supply. The unit can be checked from inside the coach by an informed technician. I know this doesn't help much but it is a start.

Reagan