Since you have an intermittent problem, it will be difficult to trouble shoot. What I would recommend is that you, or someone comfortable with electrical wiring, start at the source of the 120 vac supply and ensure all connections are clean and tight; all the way up to and through the distribution panel and inverter. Then start at the battery banks and do the same to all the loads. This will take some time but I think you may find some loose connections that will be the cause and fixing them may correct the problem. Good luck and keep us posted.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7