Thanks to everyone for the advice.
I am going to go into seclusion if it ends up a loose battery connection, however.
I am pretty positive it is electrical since we had problems all last summer with the alternator. That issue was resolved when the alternator shop discovered a loose wire inside the alternator that would lose contact when hot and kill the alternator. But we replaced just about everything related to the alternator(wires, etc) AND the main boat battery, so I haven't been paying attention there.
Thanks again! I'll let you know what happens.