Page 41 of the 2013 MSH3012M and MSH4024 manual states charging current will be reduced if the inverter temperature is high or the input AC voltage is below 90 VAC. It also states low charging rate with a generator can be caused by low power capacity of the generator. Maybe your Yamaha is acting up at low loads?
Come to think of it, one of my Yamaha 2000 was doing the same thing. It would stutter and spit at low wattage loads, but run a space heater just fine at full speed. That really confused the Magnum since it likes to "ramp up" its charger load (part of the pfc circuit I think). The generator would reject the light load and the so magnum wouldn't qualify the generator as a suitable power source (blinking charge light on the ARC.) I switched to my other yammy and everything was normal. Back home I ran a lot of carb cleaner and a tank of fresh gas through the yammy that was acting up and it recovered.
MrWizard: From page 43 of the manual:
AC input voltage range 60 to 140 VAC (120 VAC nominal)