It sounds like a typical short. The next time it starts, go to the converter and listen. If it is something shorting out, you will hear the converter straining to keep up.(it will get louder each time the lights dim) Start by turning off one 12volt light at a time. If it still happens next remove one house 12volt fuse at at a time. Finally remove the battery cables one at a time. This will tell you which area you have a problem. also check at the converter output wire. many times they put in a 12volt automatic circuit breaker. these can get weak and cause this problem.
1998 Pace Arrow 35 ft. F53 Ford V10 2012 Honda Civic toad
15 year motorhome service manager. 3 popups....2 travel trailers....5 motorhomes....loved them all.