When you say it takes 20 - 60 minutes until you can restart the gen.... does it crank and not start or won't it even crank? How long has the AC been running before it shuts off?
A couple things I can think of to consider....
1) Possible heat issue. The AC is probably the biggest current draw so perhaps the load is causing the generator to get too hot causing the shut down and then it has to cool off to restart. Might be worth checking that the cover is on the generator is tightly sealed for proper air flow and cooling for the generator.
2) My generator will not run when the gas tank hits 1/4 full. Maybe a grounding issue is causing a false fuel level signal to be sent when the AC shuts off.
Definitely a strange one....
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