Late 2011 13" MacBook Pro doesn't detect external monitor anymore on Mavericks
Seeing that this question has become popular, I will tell you how I resolved the issue...

I was using a fake adaptor, but it worked with Mac OS X flawlessly for two years. Strangely, it only works now when booting with other systems (like xubuntu live cd).

What I did to solve it was buying an original adapter from Apple.. I hope it will last until my Macbook becomes useless..