Problems with the windows on Mini Coopers are not uncommon. Several issues have been reported with the motors on the window burning out and leaving the window stranded in whatever position it was last in. There are a number of solutions to the problem which you can try yourself before taking the car to the dealer which may be useful, particularly if it is not under warranty. You can recognise a problem when the window stops dipping when you open the door.
Put in the key and turn the ignition on but leave the engine off.
Hold the window button in the up position for 10 or more seconds.
Open the door to make sure the window closes correctly and test the window for normal operations. Dipping of the window is the small drop down when you open the door and the small jump up when you close it again. If the window still does not work then move on to check the fuse.
Open the fuse box. You can find it using the Mini's owner's manual.
Remove the fuse for the windows.
Check the fuse and replace if needed.
Test the windows for proper operation. If they are still not working then check the motor connection.
Turn the engine off and remove the key.
Close the door while sitting in the driver's seat.
Tap on the door firmly with a closed fist just above the speaker.
Test the windows for proper operation. If this does not work then take the Mini to a repair shop to have the motor replaced or replace the motor yourself.
Sometimes the problem will occur when the temperature is high and disappear when the temperature drops again.
Be careful when removing the fuse, fuses are fragile and you don't want to break a good one while checking it.