I have a 94 E-320 and experienced the same problem several months ago. I've over looked checking the water level in the battery since I got the car. (many years. I thought it was a maintenance free battery and in the end it was.........)
I tried starting the car one day in my garage and noticed a slight hesitation when starting and so kept trying, to push its limit, and it died after the third try.
Check the water level and several cell were dry or low. Filled and charged for 24 hrs. on trickel charge. Started right up but after about 6-8 hours went back and dead again.
If the water level gets to low the cell plates ground out and the battery can't recover. I replaced the battery and no problem.
If the charging system is working and the belt is tight I conclude it's the battery.