Okay, with that info , I have looked at the layout of the wiring and might have some simple testing to let you get more certain of what is happening.
I did a couple little snips of the drawing to make it less mind boggling but how well that works may depend on what you are using to access the internet. If on a PC, you can get a much better look as it is larger, so take a look at this drawing snip and let me know if it is something you can see well enough to read? Try clicking the picture to see if it gets a better view!
What I marked on the first is how the power comes into the main power center on two 50 amp and those feed the 30 amp feeding the inverter power center. We can assume these to be okay as things mostly work. Just info but not needed for right now.
The second picture is the feed from the power center to this inverter panel and this is where it may help to do some testing as it comes in through a switch (on a monitor panel, etc? ) and to a 30 amp which then feeds five 15 amp breakers. You know where these are located?
The third picture is how I see things being fed by the inverter as I marked in different colors. This can get pretty messy so it may fit you better to look at the original drawing here if hard to read or make sense? Maybe it makes sense and my marking just messes with your mind, so your choice!!!
https://www.winnebago.com/Files/Files/Winnebago/Resources/Diagram/2007/07_r40fd_wire_157677.pdf
I am assuming it is the 30 amp at the inverter panel which is tripping? That would make me want to verify that there is not something drawing way too much current out on one of these lines. One way to do that would be to turn off most things by opening all the breakers but one, maybe the microwave and then try the microwave by itself. If the breaker trips, it is either too weak or there is something wrong on the microwave circuit, so I would then turn the microwave breaker off and put a load on the other circuits like one of the heater that will draw something like 12 amps if they are 1500 watt heaters. Two 1500 watt heater combined should not be enough (24 amp?) to trip the 30 amp if it is not weak! Two heaters and a microwave 24 plus 10+ is likely to be a problem if all at one time.
I suggest playing with turning things on, loading that circuit and then let it set for a bit to see if it trips too easy. Theory says that if there is a wiring problem, it should only be on one circuit so swapping around tells you if that is true and which one.
I might guess that the breaker IS weak but and the pro way to test would be to use a meter to test amps on each circuit but that gets into buying tools that most of us don't use often enough to warrant buying.