Why are you trusting the low voltage alarm on the LPCO detector? Its voltage calibration may be off, and it almost certainly has a simple threshold alarm which doesn't allow for voltage drops below that threshold when there are large power draws.
Next time it goes off, use a reasonably accurate meter to check the voltage at the battery when no large loads are on.
I said it before, but wiring it so it's closer to the battery may make it work more reasonably. Or, it may just be defective. You need to measure the actual voltage at the battery to tell.