Lo DC on fridge

The correct answer would be to find out why the batteries are not being charged. Like a previous poster said it is highly unlikely that the refer was wired to the chassis batteries. But a way to find out is disconnect the house batteries either through the disconnect switch or remove the negative battery wire. If the refer stays on then it is wired to the chassis battery. If the refer is wired to the house batteries then you need to find out why they are not being charged, either your inverter or converter is bad. If your refer is in fact wired to the chassis battery bank, some manufacturers didn't charge the chassis batteries when on shore power. In this case install a "Amp-L-Start or a Tric-L-Start". They are easy to install and not that expensive. Either one of these will keep chassis batteries charged while on shore power with the amp-l-start doin a little better job. Also go buy an inexpensive ($10.00) digital volt meter and keep it in your MH.
Blessings; kdk