Hi I have a 2002 540i. When the car is cold it drives fine, but after a little hard exhilaration or driving in traffic the transmission kicks and rpms fall bellow 500. It almost feels like the car will stall. If driving it for a longer time eventually the transmission will drop down to fourth gear and will not shift into fifth, and the rpms will be really high. After it cools down it will drive fine for a while. Please help with this issue.
Tran need to get rebuilt. You either have a cracked drum, a torn o-ring, or a bad bearing. When the Trans is cold the Trans pump is able to provide the correct hydraulic pressure, but as the trans get hot it starts to thin out the atf and the pump is no longer able to maintain the correct pressure because of the leakage from one of those parts that needs to be replaced.