If you have added an additional POWER Inverter only having one battery is not a real good idea. Power Inverters eat up batteries real quick.
If you are referring to your ON-BOARD Converter/Charger as an INVERTER unit then you may need to make sure you have a smart mode type charger being used. Most of the newer trailers have this smart mode chargers since the 2012 models... You might let us know what your Converter/charger model number is...
You also need to make sure all of the fuses between the Converter/charger and the battery terminals are still functioning... Perhaps you have a battery disconnect engaged and your battery is not getting charged from the shore power connection.
I always use a multimeter at the battery terminals to check the DC VOLTS to be sure things are normal... A fully charged battery not plugged into shore power should read around 12.6-7VDC just sitting there. When you plug into shore power this reading should jump up to 13.6VDC or whatever Charge Voltage mode the converter is doing. If you don't see the DC VOLTAGE jump up at the battery terminals then your on board charger is not getting to your battery terminals for various reasons...
Something may have been disconnected from being in the shop for repairs etc...
Also from my experience with batteries if they have been discharged below 50% charge state for a long period of time they usually DO NOT recover and need replaced. You might bring this up with the repair shop... I would not start a trip with this battery until you determine it is OK...
Roy and Carolyn
I claim Horse Creek Country in Southern Ill - Momabear is from North Texas
We live in King George VA
RETIRED DOD DOAF DON CONTRACTOR Electronics Tech 42YRS
"We're burning daylight" - John Wayne
2008 STARCRAFT 14RT OFF-ROAD POPUP with PD9260C and three 85AH 12VDC batteries
2010 F150 FX4 5.4 GAS with 3.73 gears - Super Cab - Towing Package - 2KW Honda EU2000i Gen
K9PHT (since 1957) 146.52Mhz
"We always have a PLAN B"