Here is a link
to a service manual for the updated version of the transfer switch, the Intellitec 000-00803-400.
To expand a bit on what "twinboat" advised, first perform a visual inspection of the transfer switch innards with the shore cord disconnected and generator off (that is, all AC electrical sources off). Such an inspection may reveal burned contacts. If you don't see anything obvious, the next step would be to check the screws holding the wires to ensure they are all tight (manual says torque to 35 foot-pounds). Close the cover, plug in the shore cord, and see if the problem is fixed.
Anything beyond this requires checking voltages with live AC connections. If you have not worked with live AC before, I'd advise having someone else do the work as you watch. It's a great thing to develop confidence to work on your coach's electrical systems, but there's no denying that you can get injured or killed doing so.