Checked the alternator output or drive belt tension?
I had a battery that was a year old when I got my 318 but it died after two or three months of my ownership. I replaced it and it worked fine for about 8 months more until the alternator "failed". By failed I mean it was putting out 12v, enough to run the car and keep the battery topped in normal use but when stereo and blower fans were all going, the lights would dim. The battery needs 13.5-14v across it to recharge/cope with all the accessories going.
Symptoms I noticed but thought nothing of were cranking took a little time (3-4s) on cold days, and sometimes when the car started the battery light would flicker weakly (I only saw this once or twice at night, but it might well have done it when the sun made it unnoticeable). These resolved themselves after I got a reconditioned alternator (mine was an old Valeo which I couldn't find brushes for).
So the alternator could be semi-functional, but is on its way out. Or it could be something as simple as a loose/smooth drivebelt or some corroded alternator/battery connection or earth strap.
Gone but not forgotten: '87 UK 318... Carb madness!
Currently: '90 UK 525i completely stock
"Heaven for the climate, Hell for the company."