Recently ran into this issue with my air conditioner running off my onboard generator.
While at a rest area I went to run my AC off the Onan Camp 2500 onboard and as soon as the compressor kicked in the generator shutdown. Tried this a few times and same issue, checked to make sure nothing else was on and still the same issue. Pulled out my Honda 2000 and fired it up, ran the AC just fine.
The Onan runs great and will power my coffee maker or microwave with no issues, it's only when the AC runs that I have this problem. The onboard ran my AC last Summer, however, my onboard was pulled out this winter to replace the entire exhaust system (thank you WSDOT).
Any Ideas? As I said the AC runs great and the onboard runs great, just not together.
2011 Dodge Ram 3500 4X4 Crew Cab/LB, Rancho RS9000XL, Stable Loads, Superhitch and FastGuns. 2009 Eagle Cap 1050, Hickory interior with on-board generator, A/C and Honda EU2000