Michael, Bill,
One possible explanation is if you have an electrically driven solenoid valve on the propane line as part of a propane monitor/safety system it could be limiting flow if for some reason it had lower DC voltage applied when not using the shore power and charger. It seems like it should not matter voltage wise between the generator and shore power as a source however. The solenoid valve is at the exit of the propane tank with two wires on it. Check the DC voltage there with shore power on and later when you are getting the low flame with shore power off and converter on. This scenario as a cause is unlikely but if what you observe is real then it must have an explanation.....The other check I would consider is propane pressure out of the propane regulator to see if that is in spec.
Later Ed