Why does one of my monitors turns off (sleep) when I switch to fullscreen on Flash (Youtube,...)?

Why does one of my monitors turns off (sleep) when I switch to fullscreen
on Flash (Youtube,...)?

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. It's
not specific to Youtube, I have the same problem on Dailymotion for
example, but not Twitch for some reason.
If I turn off Hardware Acceleration in flash settings the problem goes
away but I'm not sure that's a good idea (any downside to having it
off?)...
Using Windows 7 professional 64bits, Chrome 28.0.1500.95 m and Flash
version 11,8,800,94. Tried with IE9 and the problem is there too. The
monitor with the problem is an Asus VG23AH.