Even if gennie is acting up like surging, it should not trip the aircon breaker. Does aircon work ok on shore power? If aircon works on shore, then I guess it is the gennie.
Gas gennies are tricky. Not only does the governor need to control rpm, but carb has to control mixture unlike a diesel. Diesel just needs to control fuel, mixture is what it is. Much easier to control a diesel.
If mixture is not right, governor can go nuts trying to keep rpm steady. And if mixture is not right, it can foul plugs. Lose a plug and and engine can't make enough power.
First thing is take flame arrestor off and make sure choke is open. With engine running, nudge throttle linkage toward idle to drop rpm, then let it go. It should open throttle and engine smoothly accel, then linkage settle out and rpms steady. If it sputters and shakes, carb mixture not right or bad plug. Try it again giving it a hint of choke. If that improves things, carb is lean and needs work. Note most of these have a fixed high speed jet, so a lean condition means cleaning the carb.
Try disconnecting each plug wire one at a time and see that each has a similar effect on engine. If you disconnect one and no change, no fire in that hole. Try a new plug.
Keep fire ex handy for all this and don't do it if you sense any gasoline smell. Ask your wife to do the sniff test, men's noses no where near as sensitive. But we all know that...
Take the plugs out and check color of insulators. If black, or if it flunked the wire-off test, get new plugs. If black, carb is running rich.
This should be some sort of Japanese or Korean car engine, so plugs are available from auto parts store.
Be very careful!! If carb is running rich enough to make plugs black, that thing is making GOBS of CO. Very dangerous.
Also be careful pulling plug wires on a running engine. High likelihood of getting "bit" by 40kV. Not usually lethal, but will be memorable. If your heart is weak or being run by sensitive electronics, may want to refer this step to a young punk.
If unit runs well, passes the above checks, but bogs say 10sec after successfully accepting load, sounds like fuel restriction. Acid test for this is that it takes the load and runs fine until carb bowl contents, maybe an ounce or two, is burned off and not re-supplied.
Try the above and see what you get.
I'm anxiously awaiting my fish.