Your lack of warning lights concerns me. The activation current for the alternator goes through the warning light/lights. It's possible that your alternator could not be "turning on".
In looking at a diagram low oil, low coolant, low wind/wash, low fuel, charge, brake, and low pad indicators all power up the alternator with power originating at fuse# 5. ABS and O2 are powered separately.
You need those lights to work for your alternator to function properly.
Bosch Master, ASE Master, L1
33 years MB technician