Welcome! Bunch of helpful folks here.
By all means, check the condition of your batteries, clean all terminals including the terminals at the genset. From your description, my guess is that your batteries have aged unequally.
Usually, only coach batteries start your genset. Don't know your set up, but we run four AGM deep cycle 6vdc. (Our rig came with three wet cell 12vdc). All batteries in your set up must be good. Two good and one bad is almost the same as three bad.
Best to have all batteries the same age so you don't get into a rolling failure situation.
Fair Winds and Following Seas
Terry & Rosalina
2007 Winnebago Journey 34SE
Retired Navy Mustang & Navy Wife