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.
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