If you still have the oem type alternator, you probably are overtaxing it. I think you should make sure the battery hot wire and fusible link are up to snuff. Like jiggling it around a bit while watching the voltmeter, see if you notice any difference. Another possibility could be lack of battery ground, this can be checked by running a jumper wire from the alternator housing to the battery negative post. You probably have the General Motors 10si alternator which could be upgraded to handle the power drawn by the electric fuel pump and computer. I think you should be able to bolt in a 12si model from a newer CJ and get one that is the 78 amp version that was for CJs with air conditioning. If you want to really upgrade there is the GM CS130, that was designed to handle the fuel injection and A/C, but that takes a little rewiring. There also could be a short somewhere also that can be checked with an amp meter between the battery negative wire and negative post.