That sounds like the classic hdmi handshake issue. Frankly and because the HDMI chips can't be reflashed to a version that fixes that you should return them without delay and try another model.
I rarely write this but if this is HDMI, move fast. Save what hair you have.
I have an Alienware laptop with an Nvidia 260M video card. When home I have used a 24 inch Samsung monitor as my display with no issues for at least 2 years. Recently I decided to purchase a larger monitor so I bought the Samsung S27B350H at Sams Club.
The first night I used it the unit was spectacular. However the second day it started flickering badly, soon thereafter the screen would randomly go black (power indicator on the front of the monitor still on). I found through trial and error that if I unplugged power from the monitor for just a couple of seconds it would fix the issue for sometimes an hour or more. Ultimately however it would start doing the same thing again. I did install the specific driver just in case that would help but it did not. I am set on 60 refresh and graphics are set to 1440 x 900. This is as high a resolution as my card supports. While 1080p is optimal for the monitor it should not cause this issue.
Considering it was new I returned the unit and exchanged it for another of the same. Brought it home and voila......same issue. Again if I unplug it for even just a few seconds when the issue occurs it fixes it.
It seems bizarre to me that two different units could have hardware issues that are identical. It does though lead me to believe its hardware based on the power off / on fixing the issue. Any help is appreciated.