The same problem plagues me. The external monitor turns on/off intermittently and it seems to be getting worse with increased repeated instances over time. The external monitor blinked on/off twice while writing this response.
I am using a SP4 (i7, 16gb, 256GB) with a docking station and a Monoprice 28-inch UHD Select Series Matte 4K external monitor 60Hz. I have two surface docks and two identical monitors. The SP4 is on auto updates. The cable connection is MDP to DP on the monitor. I use both the SP4 and external monitor concurrently as one continuous display. I have not tried using the external monitor alone (this defeats the purposes, since I need/want both displays).
This problem started immediately after using the external monitor 6+ months ago. At first, it happened occasionally, and I assumed that it was a docking station issue. Both of my docking stations have been replaced under warranty, with no fix.
I have tried various MDP to DP cables, software repair tool, and dock repair, with no fix. I have tried swapping monitors and surface docks, with no fix.
The blinking was so severe a couple of weeks ago that I started plugging the DP cable directly to the SP4, bypassing the surface dock. The problem was better at first, but still persists. This technique created a new problem. Since using the DP port directly on the SP4, I now cannot get the external monitor to display when the DP cable is connected to the surface dock. Now, when the external monitor is connected to the surface dock, everything flickers (as if searching/recognizing the external monitor), but the external monitor stays black and Windows 10 does not recognize its existence. I bought the surface docks to use external monitors, and I now feel like I now own two $180 paperweights/chargers.
I have connected another SP4 (i5, 8GB, 128GB) that I own to the same surface dock and external monitor, and everything appears to work well (though not tested over time).
I have no idea, but this string and others online indicates that this is a problem with the i7 and possibly its graphics card/configuration. I also agree that it might be worse when the SP4 gets hot. And I think that I have noticed that it seems to be worse when I have multiple windows of MS Word running on the external monitor (?).
I had to warranty replace my SP4 i5 a couple of months ago, and it was a major PIA. I am more likely to but a new machine rather than replace or restore/reset/reinstall Windows. I have called and visited MS store with no success.
I am local to Redmond, and more than happy to bring it over to MS to troubleshoot.