Dell External Display suddenly stops working - Puzzling I have an early 2013 MBP, with Mavericks installed. 

I always used my Dell U2771 external display connected with a mini Display Port to Display port with no problems

Except for the last one month.

When I come to work the external screen works perfectly but after approximately one hour it suddenly goes black and whatever I do I cannot get it back to work again. I have to wait until the next day to make it work again in the morning.

When the external screen turns black the laptop still recongnizes the external display, and if I disconnect the cable and reconnect it the laptop enters the multi display mode. but without actually sendind the output

I know that the problem is not on the screen alone as I can connect other computers to it.
I know that the problem is not on the cable as different cables show the same problem.

What do you think might be the problem and why this strange behaviour?

I have a suspicion that maybe the problem is a temperature related one, maybe something in the pin of the mini Diplay Port expands when it gets hot and breaks some connection.
This would explain why it stops working after the laptop gets warmer, and this would explain why the laptop still thinks it is outputing for the display.

Or maybe this is just my head.

I think I should also mention that I have had an Apple authorized repair shop replacing my logic board 3 months ago. It is still in the warranty, so what should I do?

EDIT: after 5 months and a substituted logic board the problem remains. So this discards the temperature hypothesis.
Your issue is in Macbook's powering.  

If you unplug the power adapter and then reinitiate connection to the monitor by either turning the monitor on/off or replugging the Display Port cable, you'll see signal restored.
After that you can plug the Macbook's power adapter back again and it won't turn black for hours or even days (unless you use cheap "Chinese" power adapter -- that can blackout every 30 minutes or so). The only issue remaining is that if you use custom calibrated color profile after such reconnection the color profile resets and you have to open Monitor settings and just open the Color tab to reapply settings -- you probably can make an Automator script for that routine and bind a keyboard shortcut.

I've noticed that monitor can go black when my fridge in the next room turns on, so it's definitely about power. Seems like Macbook passes some bad electricity signals from charger to the Display Port.

"source": my comment to this thread http://en.community.dell.com/support-forums/desktop/f/3515/p/19658656/20922700#20922700