You want to check out the auto transfer switch, I have had them fail and do what you have described. There are contact points in there and they do not last forever, particularly if connected or disconnected with a load having a high power draw turned on at the time the switch opens or closes, this can cause severe arcing. Never have any high draw equipment turned on prior to starting the jenny and never shut the jenny down while pulling a load.
'98 Southwind 34L, too many cameras, old hat, young heart.
May the light be with you.