The main breaker needs to be on for any power to flow to anything.
There is no polarity in AC power. No positive and negative. What you have is Hot (black or red), neutral (white), ground(green or bare copper)
So you need to leave the main breaker on. You would only switch off branch circuits. You need to switch off the branch circuit that powers the converter to avoid a charging/inverting loop that will just drain the battery.
How is the converter connected to power? Plugged into an outlet? Or tied into the wire connection direct to the branch circuit breaker? Picture of the wires would help. Model number of the power panel and converter would help.
When I say to separate the converter wire from the circuit and move to a separate breaker... I mean to actually go to the hardware store and get a new branch circuit breaker (15 or 20 amp) and pop it in. Then connect just the converter hot (black) wire to this new breaker. This new breaker should be off when using the inverter. Main breaker is always on.