Macbook Air doesn't recognize external display Problem

When connecting an external non Apple Display to my macbook air with an VGA to thunderbolt adapter the external display won't show my Desktop. Instead it will only show for a second my desktop and then go black. 

Analysis

My mac knows that there is a display connected as I can see from the display settings. 

When not mirroring my Desktop I can actually move my windows over to the second display, but the actual display stays black, just plain black (but it is still on and active as I can see from my display status light).

I was able to reproduce and log the problem in console. The log shows following actions: 


I am logged into my account and plugin the VGA to thunderbolt adapter cable with the external display connected
My MacBook Air notices that a second display has been plugged in and switches it's display mode.
My external display shows for a moment my desktop and the turns black, but stays active (The external display status light indicate this to me) as if it would be still showing my desktop


Console Log error black display @ pastebin.com

I was also able to log what happened when my external display would finally start to show my desktop. If I am not mistaken I have just plugged out the VGA to thundebolt adapter and changed from mirrored display to not mirrored. This is what I have been doing afterwards:


Plugin the VGA adapter cable with connected display
The extended desktop shows up on external display


Console Log display recognized @ pastebin.com

Temporary solution


Fiddling around with mirroring and not mirroring the display can
sometimes solve the problem
Pulling out the VGA to thunderbolt adapter and plugging it in again can sometimes solve the problem
Plugging out the electricity for the external display can sometimes solve the problem
All actions above combined in different order can sometimes solve the problem
Solution: Buy a new Display, the old one seems to be broken

I tested my laptop with another display and there weren't any problems with other displays so my conclusion was that the display has to be the error (the display is old and used up).

NOTE: Sorry that I didn't answer my own question, I forgot about it.