I'd say that you want to make sure all of the 12V distribution panel is connected securely to the positive and negative phase power wires. You may have a post terminal where the converter wiring is connected, along with the distribution panel. Check in that area. Having drop outs and intermittent fuses blowing sure sounds like failing connections. Also, make sure you battery connections at the terminals are all clean and tight.
With your meter, you'll be able find any voltage drops that will indicate a poor connection. Likewise, your meter will turn up any opens or missing continuity.