Hi, I had a similar problem with my 2001 4.4i Auto X5. It would go to 'FailSafe Mode' after a couple of hours drive occasionally but it did not indicate a 'FailSafe Mode' on the cluster. I had it diagnosed at my dealer but no fault code relating to the problem appeared in their system.

After a lot of research I decided to change the 'Output Switch' which is located on the right-side of the gearbox. It also known as 'Range Switch'. Inside the switch there is a circuit which monitors the position the gear is in. When it becomes faulty, it will become intermittent in some cases it will not sense whether you're in neutral, reverse or even drive. When that happens, your gearbox is likely to misbehave intermittently.

To cut the story short, I purchased one from the 'stealer' for sum of £170 and installed it by myself. Less than 10 minutes job, held by 10mm bolts. Try replacing it because it worked for me. Hope this help...