Have you tried using any of the other video outputs from your graphics card (try HDMI or DVI if you can), and also have you tried any different video inputs on your monitor? If you have another monitor available, do you get the same problem on that one using the same cable and video output?

Make sure your Monitor does not have a "deep sleep" mode --> look in the Monitor - on screen Settings Menu
 
If Device Manager in Win 10 lists monitor as "Generic" -- see if you can download a Driver for your monitor

Cool GTX
Make sure your Monitor does not have a "deep sleep" mode --> look in the Monitor - on screen Settings Menu
 
If Device Manager in Win 10 lists monitor as "Generic" -- see if you can download a Driver for your monitor

Just made the changes well see what happens 

I have a few more questions. First of all though, did the HDMI cable have the same loss of display output issue?
- If the HDMI cable works fine, swap back to DisplayPort and test if you loose the display signal on 60Hz or on a lower resolution.
- When does the display output disappear? Is it at completely random times or is there anything in common (like high power draw or opening a particular application or something)?
- When you loose the DP signal, if you unplug the cable from the GPU or monitor then reconnect it, does it re-initialise the signal or does it require a system reboot to fix?
- Is the GPU hitting any kind of power or temperature limit?
- It is probably unlikely, but its always worth a check; is the GPU seated correctly in the PCI-e slot, and are the power cables connected correctly? Check to make sure they aren't loose.
 
Edit:
Something else I just thought of is to try pressing Win+Ctrl+Shift+B when you loose the display signal. The keyboard shortcut should reboot the graphics driver (which can be very useful in some situations). See if this brings back the display.