We have a single Coleman Mach 15 A/C on our 30 Amp Class C. On a recent trip, the compressor began to cut out after a longer time than yours, more like 20 minutes. Then it could re-start after about 20 minutes to cool off. It was not dirty (have you cleaned the coils on yours?) and was not freezing over. So I tested the Compressor Run Capacitor with my Fluke Meter. Tested Good. Since I had a new spare capacitor on board, I swapped it in. Compressor kept running and sounded better also. I just bought a new capacitor to have another fresh replacement. $15.80 on Amazon, free shipping.
Amazon Link Here40 uF for Compressor combined with 7.5 uF for Fan. Make sure the values match yours. I can't come close to a promise this'll fix it. Odds favor a failed compressor, but for under $20 (maybe $30-something at an appliance parts store) it's surely a cost effective try.
If you want to try this, check back with us on how to handle capacitors.