First, since this is your post #1,
If your RV has a single output "dumb" converter, it can overcharge the batteries and boil them dry in a matter of a few days or weeks at most if left plugged in continuously.
On the other hand, if you have a multistage output "smart" converter such as the Progressive Dynamics 91XX series with Charge Wizard or 92XX series (XX = output amperage rating), the converter will taper off the charging voltage as the batteries recharge. With the PD9180 converter and Charge Wizard, we leave our 5th wheel plugged in 24/7 while it's in storage and only have to add water to the batteries perhaps twice a year, even in the SE Texas heat.
It sounds like your converter has packed it in. If the service facility verifies that, here's your opportunity to upgrade to a "smart" converter as a replacement. It's well worth it!!
And, yes, converters can quit any time, usually at the most inopportune times. Our first converter failure was in the Gatlinburg, TN area in late October 1996 with nighttime temperatures in the low 40s. The tipoff was when the furnace quit running in the middle of the night when the coach batteries discharged!!