No, " The converter " converts 120 volts to 12 volts for lights, water pump, heater fan, ....
The microwave is strictly 120 volts along with the air conditioner. The converter has nothing to do with them.
First check is the plug on the shore cord. If it can be opened, take a look inside for loose wires. If that good or a molded plug that don't open move on down the wire.
If your trailer has a cord socket built into the out side wall, there are times when the wires behind it get loose.
You may need to pull the receptcal out of the side to see if the wire connections are tight.
If the shore cord wire just goes into the inside, you will need follow it to the breaker panel and check the connections in there.