YC 1 wrote:
On some Inverter/Converters there are AC circuit breakers for the inverted outlets. You should be able to measure AC voltage at the inverter by removing a safety cover.
In short, AC may run to the inverter/converter and pass through when not inverting. When Shoreline is gone the inverter kicks in and supplies power via a circuit breaker path.
After reading your symptoms again I'm thinking your shoreline outlet breaker popped, then your inverter ran the rest of the night and your batteries were run down to the point the heavy load of the coffee pot put it into a shutoff mode.