if you leave your motor running like i do then your alternator will keep charging the batterys nothing to worry about, and also some inverters shut off before the batteries run out to keep enough charge *to start, if you do turn your motor off.

yall have different electrical set up than i do. both my batteries can crank and they both can supply power to the things the alternator can't. i am not sure if a boat is like a car but the batteries main purpose is to start the motor then the alternator runs everything. the batteries can help supply power but they cant do it for ever, even with the alternator charging them. ;)