Unless you modify the Power Plan settings for the Surface Pro, one of the more frustrating pieces is the way it sleeps after a period of screen inactivity to conserve battery. If you're watching a video (example: Youtube) the screen will shut off. The default Power Plan settings to blank the screen is 2 minutes.
You can go into the Power Plan settings in Control Panel and adjust how the Surface Pro reacts based on whether or not it's plugged-in, but, if you want to keep the settings as they are, yet still enjoy uninterrupted video, try utilizing an app that forces the screen to stay on.
In my example case, I was watching Windows Weekly 310 last week and to keep the screen from blanking during the video, I snapped my favorite Clock app next to the video window.
When I'm not using the Surface Pro, I allow the Clock app to run, giving me an instant view of the time and date. Snapped next to my video of choice, the Surface Pro stays alive, allowing me to watch the entire video.
Incidentally, it's the same Clock app I've talked about before in the following article:
In the future, I hope Microsoft adds the ability to detect if video is playing or not, and allow you to customize what the Surface does based on the screen activity. Android tablets are smart enough to not shutdown during video playback.