If both batteries have been tested and are in good chargeable condition, and converter/charger is supplying 13.6 volts charging voltage measured at battery terminals, and you are allowing enough time for converter to charge both batteries, there may be a short in the 12 volt wiring system or some item that is drawing excessive amps and needs to be disconnected/replaced. Check for lights left on in the storage compartment, etc. If there is a short, it should blow a fuse or circuit breaker if one is in the circuit, if not, a short could cause a fire. You might try feeling for heat in 12 volt wiring. If you had an amp meter, you could check on how much current is being drawn from batteries with everything shut off.