Monitor does not wakeup, but SSH access is possible

After some idle time in GDM the Display turns off, and does not wake up when I move mouse or press some keys on the keyboard. But I can access the system with ssh. When trying to reboot the system with “sudo reboot” the ssh connection closes but the computer does not reboot. Maybe it has something to do with the graphics driver? I have an AMD graphics card.

How can I find out the reason for the problem?