[bmwtech]

Does your Z3 have the OBC? Sometimes they will start to short out and draw constant power. I had this same situation happen to my e36 M3, thought I was not driving it enough also until I ran some tests and took a random shot at the OBC. I just unpluged it and problem was solved. Drove me nuts! I'm not saying this is the problem because there are numerous things that it can be, good luck!