Some things are simple some not!
Maybe the plug is not making good contact, so wiggle it to see if things jump up?
Maybe the cord has a bad spot? does the place where it goes into the plug look like the end has been twisted too many times and the wire inside might be broken?
But if you want to get into testing after looking, the transfer switch is a very likely place to go.
Idea is simple with the generator as I've marked with black OR the cord as marked in red, the switch chooses which is good and passes that one on to come out to the load center as marked with blue!
click this drawing to see better!
So if you make sure to unplug the cord and kill the generator to remove all AC power, open the cover and do some looking.
Clear out anything that looks out of place like ants, wasp nests, etc. and look for signs that something may have gotten hot.
Any signs of arcing, black spots, or melted insulation to show where something may be wrong?
One biggie that is semi-common is one or more wires getting jerked up and down as we hit bumps and eventually they can get pulled loose and then power starts jumping across the gap like an arc welder!
Sometimes easy to see but if not, just go for a big screwdriver and tighten all the screws that hold the wires, just hoping to prevent it later?
But if you find nothing, a meter is needed to check the voltages on each wire coming in and going out to the load center.
If you start at the wiring going out to the load center and the cord plugged into a good outlet, there should be the white wire (marked in blue?) as neutral, so touching the other probe to either the red or black should show near 110Volts AC. Make sure both read near 110 for two different legs.
Thats is the power going out to the RV load center!
But since you find it not working, I would assume you won't get the 110 AC on one or both of those points!
If good there, the problem has to be toward the load center, but if it works on the generator, the problem should be right there in the switch.
So check to make sure the power is coming into the switch on the wires I marked in RED!
Again, center is neutral and red and black wires should be hot and near 110!
Theory says you are real close to the problem but that needs testing before trusting what I "think" !!!