This is caused by a non-compliant Displayport cable that sends a power signal from both the sink device (your monitor) and the source (the video card) over pin 20. This causes a short which results in random issues such as the monitor cycle on and off, not start up at POST, or the monitor randomly powering on or off. Most Displayport cables, including those provided with your monitor, do not meet the Displayport certification for single monitor use.
You can test your Diplayport cable's pin 20 with a multimeter to see if it has this issue. A properly certified cable should register 0.0v on the 20 pin. If you register any voltage on pin 20, usually between 2.0 and 3.6v, then you will need a certified cable to resolve the issue.
You can find a list of certified cables at www.displayport.org.
These issues may also be mitigated or eliminated by adjusting settings on the monitor itself:
1. Disable Energy Smart or Eco Mode
2. Set the monitor to Displayport 1.1 or disable Displayport 1.2 (Note - this will limit monitor refresh rates at higher resolutions and may not be ideal)
3. Manually set the input method to Displayport