Am very suspicious of "alternator tested fine".Any car this age requires a
permanent in dash voltmeter,its always my first "mod",so you can see whats happening live at all times.Alternators can "test fine" and have all sorts of issues. Car can run fine but still not have enough power for restart next morning.Plus battery has been drained a few times so it has permanently lost lots of capacity.That being said as others mentioned parasitic drains should be eliminated, connections checked, cleaned.Stock 240 has very little parasitic drain,See BMW forums(my case E53&E46) for real parasitic drain issues.
P.S. is alt belt snug enough?
GOOD LUCK
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Rene
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