I assume it is tripping the GFCI not the actual circuit breaker, yes?
If so then there are a number of things it could be:
1) Your GFCI receptacle might be getting weak. If they trip a lot they tend to get more sensitive over time. That is possible but unlikely. Test that by plugging into a different GFCI.
2) Your extension cord might have an issue. A frayed place in the insulation might let enough moisture in to trip the GFCI. Test by trying a different cord.
3) Your extension cord or adapters might not be making contact properly. If the plug is worn and has overheated it might be arcing internally. It could also be the input port on the rig where the extension cord plugs in.
4) GFCI's trip when there is an imbalance between hot / neutral. So you could have a neutral wire in the rig touching ground someplace. Possibly in the circuit panel or converter. Hopefully not in the wall someplace.
5) Your converter might be causing the issue. Some converters leak enough voltage to ground to set off a GFCI. Not much you can do about that except replace the converter.
6) RV's rattle everything in them so it might be a loose wire someplace. Check the breaker panel and tighten down anything loose. WITH THE POWER OFF!

To see if you can isolate the issue turn off all breakers in the RV. Plug in and see if the GFCI trips. If so that indicates an issue before the circuit panel. If it doesn't trip then one by one turn on the breakers until it does trip. Then figure out what is on that breaker.