I have been using dual displays with my Surface Dock and Surface Dock 2 for awhile now, but recently the second external display would just go to sleep and not display anything no matter what I tried.
The solution was found in a Microsoft forum.

Clear your display cache.

1. Undock your Surface from the Surface Dock.
2. Download the Surface Dock registry file. Choose to Open the file.
3. Select and run surface dock registry.reg.
4. Select Yes to allow changes to your Surface, select Yes to confirm, and then select OK to close.
5. Restart your Surface, reconnect it to the Surface Dock, and try your external display again.