The "main grounding point at the converter" is for both 12v and 120v ground to frame. This can make for some strange things.
I have an inverter with non-GFCI receptacles and I use the shore power cord in that for "whole house." (converter off) This works great, but now the neg wire battery disconnect I have has no effect, because the shore power cord neg wire is making a 12v neg path from battery to DC dist panel.
Another inverter I have does not do that, with its "floating neg" GFCI receptacles.
Of course if the battery disconnect were on the pos wire, like many are, that would not be an issue.
On a deck-mount converter, which has a chassis ground lug same as an inverter does, when you look inside, you see the 120v power cord's neg wire goes to the converter's chassis (not connected to the DC output) The chassis ground then takes that to the frame. An inverter is arranged differently inside, but the point is that funny things are possible.
I would still think an intermittent problem would indicate it is not a standing problem with the set-up, but a loose connection.
