Hi Lance
I've had the 2KW PF heater since 2010 and although it's a fantastic hot water heater I'd always had problems powering the heater with batteries. I have used a variety of leisure batteries since getting it and have found that powering the heater for even short periods was very hard even if bench charging the two batteries with a smart charger every night.
It was always the two volt meters flashing "BATT" that would lead me to believe the batteries were not charged up, until recently I bought a hand held volt meter which when connected up to the battery terminals told me in fact the batteries were fully charged, for me the problem lays with the wiring behind the Flow Masters over heating including the little plugs the flow master volt meter can be reading 11.8 volts then if you wiggle the wires and plugs it's suddenly 12.5 volts. So for myself the problem is not with the batteries being discharged too quickly but the flow master volt meter giving a misleading reading. Two of us have been using hot all day for the past two weeks with no problems from the batteries, fiddle with the plugs and you'll get a more accurate reading.
I bench charge the two batteries all weekend with a smart charger and once over night mid week if the heater is being used for more than a few days. As soon as I get chance I'll be getting the wiring behind the flow controllers up graded so they don't heat up.
The batteries I use are beasts and not cheap at over a hundred pounds each, I'll get the spec on the batteries for you tomorrow and post on here if you like?
Hope some of this makes sense and may shed some light on your charging issues