Although I have never worked on a BMW DVD/CD unit, in the past I have worked on loads of domestic units in Hi-Fi and TV set ups. If you have, or know someone who has a CD/DVD cleaning disc, it could be worth putting it in, but they tend to fix faults like skipping/jumping due to dust on the lens, so I wouldn't go buying one and expecting it to cure all. When a unit fails to recognise that a disc is in the unit, it is usually the laser, the focal unit or a sensor on the drawer mech, but it could also be the electronics in the unit itself that controls one of the items that I have just listed, it is a fault that could be caused by anything to be fair, even a disc where the back printed label has been scratched can cause the problem.
If you know a local TV engineer, they may be able to help, but they are becoming a rare breed due to our "throw away" society of today, and you would also have to remove the unit from your car, (I'm sure that I have seen something on You Tube that shows how to remove the screen and DVD unit).