Macbook Pro connects an external monitor only after reboot
This is the solution:

The 15 inch Macbook uses 2 graphics cards. I use gfxCardStatus application to control which graphics card is used - OS X too easily allows apps to request the more powerful card, which drains the battery too quickly. Skype is an example of such an app.

I just discovered that the integrated graphics card (the weaker one) cannot support a second monitor for some reason. Even though in my 13 inch Macbook it can. So only the "discrete" (or the more powerful) card can do this.

In essence, either stop gfxCardStatus app or go to "Discrete Only" mode in it.