Strange Problem!!!

Take them back for a check. They should be pro-rated. Sometimes they go bad. It may have been built on Tuesday after a 3 day weekend in the RV.

Intermittent problem. Let it develop.

These are 6 volt batteries. should they be 12 volts?

Just checked with Monaco, house batteries should be 4 6 volt batteries.

First step is ALWAYS inspect, clean, reattach battery connections. Check each battery individually with a DMM while they are disconnected. Better still, use a hygrometer for each cell. More likely an install issue than a bad battery but at this point everything is still on the table. I don't remember what the charging voltage should be, but I think it should be higher than 6.2 when it is actively charging a nearly full bank. Continue to gather data and report back.

If you turn on shore power, what happens? Does everything work but the water pump?

With shore power on, the converter is supplying the 12 VDC and the batteries are basically just redundancy. So for now skip checking the specific gravity and all that and reconnect the shore line. Does the pump have 12 VDC? If it does then the pump is most likely bad. If there is no power to the pump, then you need to determine where the fuse or circuit breaker is and check for power on both sides of the fuse or CB.

If this doesn't make sense to you, I would suggest a mobile tech. If you're in a campground, ask for a recommendation from the desk clerk. If you are at home check Google or the Yellow Pages for one.

Extreme heat or cold can cause strange things to happen to electrical devices. Extreme cold can freeze water, could your pump be frozen? Is the pressure sensing switch on the motor bad? There are a lot of variables and that is where experience comes into play. If you don't have it call the moble tech.