Power Drain

Sorry this is so long.  I was lucky enough that all trailer systems seemed to be working for a couple of years (except for day and night shades), so I got out of the habit of checking in to the forum discussions.  Things seem to have changed.  But now I have a problem that I can't figure out, but someone else might have an answer.  Last week, when I used the trailer (a 2004 SunnyBrook Titan 5th wheel), I woke up to no AC power on the second morning.  The trailer batteries were okay, so I didn't even notice this until the coffee maker didn't work.  The trailer was plugged in to a solar power system, so I started there.  As best I could tell, the solar batteries weren't dead, but they wouldn't start the inverter, and the controller screen was blank.  I eventually got the system running, but the inverter showed a 400-watt load.  This load disappeared when I unplugged the trailer.  So, I turned off the inverter, left the solar system to recharge, and started a generator for the trailer.  The following night, I measured the voltage drop from using the heater while in bed.  The loss was not quite 1 volt (from about 13.7 to over 12.7) from two 100-amp AGM batteries in parallel, which calculates (crudely) to about 40 watts per hour.  So, I seem to have a 400-watt, continuous load from somewhere between the trailer plug and the trailer batteries.  400-watts for 24 hours comes to 3600 watts per day.  This is more than the solar panels produce through winter's fog, clouds, short days, and long nights, not counting my own use, which explains why the solar batteries were low.  All that I can find between the trailer input cord and batteries is a transfer switch and the power converter.  Is this a symptom of a dying power converter?  Can it be tested with the converter still installed?  Any thoughts would be appreciated.