Yes, all the advertising is in watts, then when you look at the Owner's Manual specs it's suddenly VA. In the case of the air conditioner and water heater I doubt that makes much of a difference. In the one air conditioner I measured (I'm assuming they're all similar) the VA draw was 7% greater at the high end of the voltage range and 2% higher at the low end. I'd suspect there's more to the story: maybe a weak generator, another power consumer you're not aware of, or high altitude. My eu2000i starts to degrade noticeably at 3,500 feet when it's hotter than 90. You could track it down with a kill-a-watt on the generator output, just not with the a/c and water heater on at the same time. I can't take on the battery question. There could be something like a timer on the inverter, then again maybe not.