If your A/C is a 15,000 BTU unit then your total current draw could be around 16 Amps +/-, and the microwave mighr draw as much as 10-12 amps but I don't know the type/size of your microwave. As the A/C units cycles off and on there will be some "inrush" current upon restart that, combined with a microwave running at maximum wattage, could be enough to exceed the upstream breaker's (pedestal or generator breaker). The previous post about knowing the actual loads running and having a way to neasure that load would go a long way in diagnosing the problem.
You may not have a loose connection but it wouldn't hurt to have all electrical connections checked either by a knowledgeable friend or a licensed electrician/technician.
Good luck,
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Ed & Robin Lively
with Nina, Kitt, and Mickey
2016 Thor Synergy TT24 (a.k.a "Ming")
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