Member, Sport: Off DSC: On (>50 posts)
Join Date: Dec 2015
Location: Alameda, CA
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Maybe check your "transmission" fluid?
Check your brake fluid, as with a 540i your brake fluid is also the hydraulic fluid for your clutch. I'd think if it was slipping like that while you were driving, you'd know about it. Of course, if you were leaking that, I suppose your question would be "why is it so hard to shift gears?" or "why is my clutch pedal resting on the floor?" but it is something worth checking.
I have a 2000 540i and right after I bought it I had a hard time shifting and actually blamed it on the new winter boots I bought -- I thought I just couldn't get the clutch to let go as my boot must have been stuck on something. By the time I got home I was running stop signs as I knew if I came out of gear I was never going to get back in. I suspected the clutch slave cylinder was leaking. Before tearing things all apart I inspected the pedal and noticed it was almost on the floor. I simply lifted it up with two fingers and it stayed up and I drove it around nervously for an hour waiting to see the problem come back. Then I drove it sorta nervously for another six months. At this point it's been about a year and it hasn't returned, at all. I suspect I had a bit of grit caught somewhere and lifting the pedal up must have moved the fluid around and whatever was stuck now isn't. I wonder if you're in a similar situation where the clutch is not engaging for some reason, especially if the car is off and the lines aren't pressurized.
If your brake fluid is low, or too high (installed new brake pads after adding brake fluid during an oil change or whatever) I can think of a couple unusual things that might happen. I myself am due for new brake pads and I'm going to flush the fluid while I'm at it which I suspect I should have done at the time but had no idea that the brake fluid had anything to do with the transmission at the time.