Why won’t my Champion C46540 generator run the microwave?

I would suspect a the generator is slowing too much and the frequency is dropping too far below 60 Hz. It could also be dropping the voltage too much. Have you measured the frequency or voltage when it's running? I'd compare it to when it's running the coffee maker as that should be similar sized load. Coffee makers probably don't care much about voltage or frequency.
Keep in mind too, if your microwave is rated at 1,300 watts that's usually it's "cooking power". It's actual power draw from the generator will be a couple hundred watts more. That's not enough to make a difference unless you're running other loads at the same time maybe.

That's an old generator. The generator total harmonic distortion (THD) many be too high or the output voltage may be too low. If may be time to replace the brushes.

Does the microwave have a loud hum when running?

That model is rated for 3.5 KW continuous, and has an automatic voltage regulator circuit - so it should be capable of powering just about any microwave oven.

Microwaves aren't particularly picky about the AC line frequency, so it should still work even if the frequency is a few Hz off.

You might try measuring the AC voltage at the same receptacle the microwave is plugged in to - while the microwave is running. Look for excessive voltage drop as soon as the microwave is turned on.

OP: What you posted for connection is not correct. The four pin twist lock is a 120/240 genset output. The 30TT three wire receptacle is 120 volt.
The twist lock only has a 240 volt output rated at 14.6 amps. See page 6 of owner's manual
You should be using the 30TT recptacle to get full load from genset.
What is shore power connection in your rig?

enblethen wrote:
OP: What you posted for connection is not correct. The hour pin twist lock is a 120/240 genset output. The 30TT three wire receptacle is 120 volt.
The twist lock only has a 240 volt output rated at 14.6 amps. See page 6 of owner's manual
You should be using the 30TT recptacle to get full load from genset.
What is shore power connection in your rig?

This makes sense. If you are indeed using the 4 pin connector to a 50A 4 pin RV cord you are only able to use 1/2 of that power for any one of the 120V devices.

Our 2000W Honda struggles with the microwave so 1/2 of 3500W would definitely do so.

Since your RV doesn't need 240V, using the 30TT will allow all of the wattage at 120V, which in turn can be connected to both legs of the RV via an adapter.

I better clarify that the twist lock is 120/240 four wire. 14.6 amps total, indicating it would be somewhere around 7 amps per 120 leg.

In addition to the output of the generator, you need to consider that microwave power ratings are output power. A 1300W microwave may use 2000W from the power source.

Also consider many split single phase generators have the AVR on only 1 phase. If you are loading up the non regulated side the voltage would certainly drop.

If the battery charger or hot water heater kicking on? Add that to lights, fridge and a few other minor loads and you could be overloading it...but I would expect a breaker to pop rather than the microwave to stop on it's own.

As mentioned, put a meter on the outlet adjacent to the microwave plug to see if you can see any voltage/hz issues. If you have a kill-o-watt device, put that in-line to see what the wattage draw looks like.

Is this a model C46540?