There are two versions of your year, early and late, so I choice early but both appear to have the same circuit on this item and it is quite simple as the GFCI come nearly straight off the load center. I've marked in green the breaker, but some basic will help sort it. One is the leftmost 30 amp breaker feeds all the other breakers in this box, so check something simple like the microwave for lights and that will tell you the power is getting to the load center box and almost certainly to the first 15 amp breaker from the left which feeds the GFCI.
If I am correct on the right drawing (check me, always!) make sure the 15 amp is working if you get lights on the micro. Try flipping it off and back to make sure as they can appear good when flipped. If that is good, power should be going straight to the GFCI, if not there is a loose wire at the breaker or GFCI, or a bad breaker or GFCI or one other. Checking for a good connection on the ground as well as the hot side is always good.
But be aware that GFCI trip when there is a "ground fault" meaning power is leaking to ground where it should not. It could be right at the GFCI or on the wiring to the exterior or bath outlets, so give a look at each of them. Not wet are they? One first stop test might be to take the wires going from the GFCI to the others off and see if it will reset, telling you the problem is on to the other outlets.
Also keep in mind to check the wiring on the GFCI for "human failures" as they do happen to the best of us. Make sure the load and line is turned the right way? And it is always possible to get a defective new one.
Drawing does not cut and copy very well so this is the original if you can access it on page four:
https://www.winnebagoind.com/diagram/2016/000200769.pdf