First, check the water level, then disconnect the ground strap and attach a charger. If it charges maybe like mine and most others, the converter does not charge the chassis battery. Or if it is convient, go to some parts house like AutoZone and they will check you battery condition free.
I decided to buy a meter and do it myself in the future.
Because the converter doesn't charge your chassis battery and there maybe significant parasitic drains, your battery may go flat pretty fast.
A question other that those asked and not yet answered, how long is it from the time you plug in until you check the battery. Is your rig stored for one week or six months between uses?
Look up "The 12Volt Side of Life", lots of answers there about house batteries and the 12 volt circuits.
I'm sort of disjointed here but remember, the more info you put down in the question the better the info coming back to you.