Headlight system fails in the night. Light turns off itself.

If you have the high intensity buls...also known as H.I.D. bulbs then it sounds like you have a bulb going bad.

I had the same problem, I first, I thought it was the ballast, which would cost $1200 to replace; since you would need to replace the entire light housing. The dealer told me that it was the HID light going out and dealer cost would be $240. You can do it yourself or even go to another shop for roughly $140.