There is likely a self-resetting circuit breaker that is failing. It could also be a component on the converter's circuit board or a combination of both.
When the converter is powered and the battery connected, the battery provides capacitance in the 12V system. The capacitance allows the converter's output and internal charging circuit to run "smoother". I'd suggest you connect the battery when using the converter and your 12V system. Monitor electrolyte level in the batteries if you have FLA batteries.
This
battery filler makes maintaining batteries easy.
