I'd be focused on that junction terminal and also the cables to/from it. I'd also take a voltmeter with you and take it for a drive. And a cellphone.
X2 on that. With a voltmeter and little luck, you should be able to find this. Not that I have ever had this particular problem, but I would suspect a bad connection somewhere. Start at the battery and start tracing the 12 volts back to the fuse block in the car (when it is dead).