Car keeps dying overnight

I've had this car for 5 years with absolutely no problems.  However in the past
month she continues to go completely dead overnight or sometimes within a
few hours. Its not every night and it happens randomly. Getting a jump seems
to temporarily solve this problem. I've changed the battery ; had it checked 3
times now by 3 different mechanics and all say its good and fully charged. I
had the alternator replaced; again everything checked out. I had the fuse box
tested for electrical problems to check for a current draw and they couldn't
find a problem. I'm at a loss as are the mechanics I continue to bring it to.
Does anyone have an idea what could be the problem? I'm desperate at this
point.