Possible loose connection somewhere in Main AC Supply wiring. Start looking at the Generator supply wiring first. On my MH there is a junction box next to Genset and with AC POWER OFF remove the cover for inspection of the Wire Nuts and Wires for loose or over heating damage.
Next, check the wire connection's on your Transfer Switching Unit, double checking wire Terminals are not loose.
Remember, work safe when playing with 120AC Voltage wiring. Unplug Shore power, Inverters OFF, Gen OFF.
Good Luck and lets us know the outcome of your mission please, after you figure it out.
