From what you have described, it is hard to say not knowing a little more info. Honda states that generator produces 120 volts, 2000 watts, which means it has 16.6 amps max and I believe the AC unit draws 20 to 22 amps of 120V power. I would check to see if any circuit breakers tripped, both on the generator and in the trailer. If a circuit breaker on the generator tripped, I would say the AC unit is drawing to many amps for that generator and you should see about trading up to a larger unit.
Remember Volts x Amps = Watts. 120 volts at 20 amps = 2400 watts. You can use this to determine how big a generator you require. If the AC unit draws 2500 watts at start up, then 2500/120 = 20.8 amps. To run your AC you need a 25 amp 120 volt power source. For a 12,000 btu AC unit, you should have 2500 watts of 120 V, minimum for compressor start up, and 1700 watts at 120 V for AC operation.
If a circuit breaker tripped in the trailer, reset it, turn everything off in the trailer and then try the AC again. You might have just experienced a spike of high current draw that tripped a breaker.
If all breakers are fine, you have an AC issue and need to take the trailer in for service.
I believe the problem is with the generator. I wanted a Honda for their quiet operation, but one that would run 30 amps was very expensive. I went with a 3500 watt Champion RV generator. It is rated up to 30 amps, but the thing weighs 100 pounds, not real quiet either, but it powers the trailer with ease.
I really hope I have not confused the issue, good luck!
2006 Nissan Xterra
B&M Trans Cooler
2011 Nomad 206
Panasonic/Pioneer/Kicker ~ Audio/Video System
Days Camped /2009 / 33