Do you have a salesman's switch just inside the door? If it gets bumped off (so easy)the 12v power to the AC control board is off & no AC. You said it worked on shore power though, and that has me looking at the transfer switch as suspect. Your 06 Monaco was built with the recalled Iota transfer switch. They are famous for failures and it's possibly the culprit.
Like 10forty2 said, it could be the breaker on the genset itself.
A good VOM is your best friend right now.
2008 HR Endeavor PDQ - Ford Edge 4 Down
FMCA F374292