What year Southwind are we talking about? Most of the older ones had no inverter at all, or had an inverter that is dedicated to the TV & entertainment cabinet. While an inverter could be the source of this problem, it is pointless to debate it unless we can be sure there is one involved.
A bad or loose wire connection somewhere between the breaker and the outlet is at last as likely as the cause of low voltage.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL