Had this problem one time and it was moisture/corrosion on the top of the batt./terminals causing a leak to ground. Another time with my current truck and it was old wiring from PO's removed CD changer that was split and causing a leak to ground when wet but not enough to blow the in-line fuse.
Removed all PO's garbage wiring installed new Batt. [1200CCA tow truck batt.] and no worries since so far as that went...