GeneratorAC weird problem... stumped

Can you post the exact model off of the data plate. I suspect this may be an early QD series generator that has a built in inverter. They work very differently from standard generators. The generator creates either split phase or 3 phase AC variable frequency electricity. This is rectified to DC and the inverter is recreating 60 Hz AC split phase 120 VAC electricity. It is possible that the inverter portion of the generator has malfunctioned and cannot provide sufficient surge current. I suspect that this is the case because you state that the generator returns to idle. A 1800 RPM or 3600 RPM generator without an inverter won't do that because the frequency is tied to the RPM of the generator. You may try this to test. Plug in a 1000 watt or 1500 watt heater or blow dryer or 500 watt halogen light running on the generator. Then try to start the AC unit. I know that it sounds counterintuitive but that amount of load will cause the inverter to ask the generator to operate at a higher RPM thus giving the AC unit additional start voltage and provide less voltage sag. In an ideal world you would put this on an oscilloscope and watch the waveform as the AC compressor motor tries to start. It is likely you will see a major voltage drop and the compressor protection circuit kicks off. The locked rotor load on a compressor is significant. You can also try a boosting transformer such as a Hughes Autoformer. That isn't a "fix" just a away to determine if the voltage is sagging so much that the compressor can't start. It will be difficult to see the voltage problem on a standard multi-meter because it can happen so fast. I would try however.