Electrical Power Issue

Rodents! In all seriousness, it is very odd you are randomly losing power to two(2) totally separate systems. Take the converter out of the coach and bench test it with a battery hooked to it and see what is does. The more you comment and we learn, the more the converter seems to be ok. Check the line and load side of your panel for proper 120 Volts. While the system if failing check the load side of each breaker to all appliances like AC, Fridge outlet, GFCI and any other 120 Volt system. There is nothing in an RV 120/12 volt system that will allow both systems to come on and off together and they operate completely separate from each other. If you lose 120 volt you will still have 12 volt and vice versa. The only way a converter will shut off when 120 volts are not supplied is ether a failed battery or the 12 volt disconnect is open. Since you losing 120 volt appliances your issue lies with that side of the system along with a potentially toasted battery resulting from a failing 120 volt source powering the converter.