I had the similar problem with my 1996 2.0l LX ââ?¬Ë?Tour approximately two years ago & it was initially diagnosed has a battery problem, however, after replacing the battery the problem reoccurred. It was subsequently discovered that the problem was actually being caused by a defective Voltage Regulator in the alternator the regulator was replaced & the problem was solved.
A few months the problem surfaced again only on that accession it turned that the cause was a defective diode in the alternator. The strange thing is that on none of the tow incidents did the alternator warning light come on indicate a problem with the charging system. I am yet to figure that out especially since it comes on when the ignition is turned on & goes off when the engine is started. Well I suppose that�s Ford for you!