I know this post is older, but thought I would respond just in case. I was having the same problem and was given the same diagnosis. Turns out that my ignition switch was sticking when I turned it off. A little WD40 in the switch, about 20 on/offs, another squirt of WD40 and 20 on/offs and boom baby, no more sticking switch, no more drained battery.

Hope that helps.

__________________
Dan
Northern Virginia
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Former Volvo Enthusiast

2002 540i 6 spd, Sports Pkg
Mods so far:
Redline MTL in tranny | Redline 75W90 in diff |
05/545i short shifter | Weighted selector rod |
CDV Delete | Zionsville Cooling Solution