2004 BMW 330i 140k miles.
We first noticed this problem a year or so ago. At first, it happened only on cool mornings if the car had been parked outside. The cold car would require 3-4,000 RPM to move, forward or reverse. After about one minute or 3-4 blocks, the transmission worked perfectly at the touch of the throttle for the rest of the day.
It only happens about half the time. Other times, even if cool and after being parked for days, the transmission engages normally from idle and up.
Once recently, it deviated from this pattern. After sitting overnight, it started and pulled into the garage normally. I shut it off for a couple of minutes to place ramps in front of the tires and restarted the car. It did not want to move on the second start. It took 3500 RPM to climb the ramps. That was scary. The car has never suddenly engaged, but if it had suddenly engaged at that moment, it would have shot me through the front of the garage.
Last week I took it to the transmission specialty shop with the best reviews in town. As life would have it, he kept it three days, driving it four times, and it worked perfectly each time he drove it. Fluid looks fine (replaced at 120k miles) and fluid level is perfect. No codes stored in transmission computer.
I thought it was intermittently draining the torque converter until this last time when it failed after being shut off for only a couple of minutes.
The transmission guy is not interested in rebuilding the transmission even if I wanted to try it. He worries that because he does not know what is causing the problem, he might invest $4500 in that transmission and still have the same problem.
All theories welcome!