I assume that's a typo for 60 Hz (rather than 6 Hz) at startup.
The governor should keep the engine speed pretty much steady, not varying greatly with load. Generator frequency, assuming it's not an inverter generator (which most or all RV generators are not), is directly tied to the engine speed; if it's 60 Hz ± a bit, the governor is operating properly.
This sounds to me more like a failure in the voltage regulation system. The "Tech Issues" forum is where you'll most likely find generator experts here; maybe some kind moderator can move this thread over there.