Wild guess. Any chance the voltage from the battery is low? This could be caused by a wide variety of issues.
- Crud on the battery terminals or any of the connectors along the way;
- Low battery charge - (charge it with a conventional battery charger and see how things go)
- Now it gets harder...bad connections to the inverter/converter.
- Check it with "shore" power connected - plugged into an AC source and with just the battery
If it's a new rig, a trip to the dealer is called for before you start messing with things, or you might void the warranty - except for checking and cleaning the battery terminals and cables.
If there is something wrong with your converter, your battery may not charge fully (or at all). And if the converter has failed, it may not pass full 12 (actually closer to 13.5) volts even when plugged into shore power.
I'm sorry I can't offer a definitive answer or more well-reasoned suggestion.
P.S. Do not plug into shore power while you have a battery charger hooked up. You need not disconnect the battery to charge it with a conventional battery charger, but you should not plug in the trailer simultaneously. As far as I understand, it's also not recommended to disconnect the battery and connect the trailer to shore power. I believe the battery serves as a buffer or shock absorber for the electrical system when connected to shore power. I won't swear to these comments, but I believe others will confirm them.