Welcome to iRV2 .
I think we have to get some terms straight , because I believe your trailer is to old to be factory equipped with an inverter.
Inverters , take 12 volt power and use it to produce 120 volt power , on some larger units they also function as a battery charger .
A converter , which is what I believe you have , take 120 volt power and produces 12 volt to power lights and charge your battery.
The converter ; should have a cooling fan that will cycle depending on how hot it is getting when doing it's job.
Have you seen the unit ?
Can you get a name and model info from it; and post it here , then maybe we can get to the bottom of your issue.
By shutting off ; do you mean all the lights go completely out , or just dim ?
Do you have a 12 volt battery installed in the trailer ?