Full screen YouTube videos in Safari log me out of OS X

I am using a MacBook Air mid 2013, 8GB Ram and with the i7 processor.

Since the update to El Capitan, I have experienced issue with full screen YouTube videos when using Safari. When I view a YouTube video in full screen, after ten seconds or so, my whole computer freezes for about five seconds, and then the screen goes dark. A few seconds later, the screen then shows the OSX log in screen, and when I log back in, all the programs that were open have to restart just as if I restarted my laptop.

Things of note:

Only happens in Safari

Only happens with full screen YouTube (full screen Netflix etc. is fine)

Only happens when the YouTube clip is put into full screen.

Does not happen with any regularity

Does not seem to matter how many/few other programs are open.

if it happens, it is always within the first 20-30 seconds of the video.

This does not happen all the time - it has just happened, but this was the first time in a couple of months - but it happened very regularly around the beginning of 2016, to such an extent that I stopped using Safari. It's really *really* odd - it only happens in Safari, and if it has just happened, it won't happen again for a few hours or days. It's also blindingly irritating as I have lost work and (more importantly) progress in Football Manager because of it. Any ideas why it happens?