Have you CONFIRMED that your inverter is IN FACT outputting AC voltage? Just because the fan/lights are on is NOT proof. For sanity, test the output terminals.
Then, with CONFIRMED voltage at the inverter terminals:
It's a simple process to pull the receptacles and check for voltage using a basic circuit tester. Start pulling the ones which are not working - check for loose wires at the terminals.
If you STILL have no voltage at the receptacles, I would suspect a loose wire junction - wire nuts not properly sized/secured... hopefully inside a junction box.
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