I also suffer from this, using NVidia graphics cards and Ubuntu. The computer fails to start the x-server once or twice each month, because of an update. Reinstalling or updating the package "linux-headers-$(uname -r)" fixes the problem for me.

You need to use Ctrl+Shift+F2/3/4/5 and switch to another tty inorder to perform these updates, as the failed x-server start leaves you with a black screen.