There are relays in the Transfer Switch that activate to direct the power from the generator or the pedestal.
I had to replace mine last year because the connections on one relay loosened over time miles. This caused heat which eventually burned through a wire. I lost all power. You might take the cover off the Transfer Switch and examine for loose screw(s) or burned wiring. I used a wire brush to clean the connection to the relay, crimped a new spade connector on the burned wire and put it back where it belonged. That restored shore power, but the relay itself was toast, so it would not switch to generator power. I eventually had the Transfer switch replaced. Make sure you disconnect shore power before attempting.
Mike