Why does one of my screens turns off (sleep) when I switch to fullscreen on Youtube? [on hold]

Why does one of my screens turns off (sleep) when I switch to fullscreen
on Youtube? [on hold]

I just got a new monitor (kept the old one as extended desktop).
Whenever I switch to (or from) fullscreen mode on a youtube video on the
new monitor (which is the main one), it turns off for 2-3 seconds, even
the backlight. Kinda like when you change resolution. If I move the same
window to the other monitor and try there, I don't have this problem.
If I turn off Hardware Acceleration the problem goes away but I'm not sure
that's a good idea (any downside to having it off?)...
Edit : OS is Windows 7 professional 64bits, Flash version 11,8,800,94,
browser Chrome 28.0.1500.95 m. I just tried with IE9 too and the problem
is the same as in Chrome. The monitor with the problem is an Asus VG23AH.
I have the same problem when using fullscreen mode on a Dailymotion video
so the problem isn't specific to Youtube. No problem on Twitch though.