Screen Standby Keeps Your Android from Sleeping While Streaming
While Minimizing Battery Usage  Android: If you use your Android
for streaming or video playback over HDMI, you've likely run
into the problem of your tablet's screen staying on
unnecessarily. This runs down the battery, and there's no need
to see the image on both screens. Screen Standby fixes that
problem.  Screen Standby simply sets your screens brightness to
zero while your streaming/playing video over HDMI. It's a simple
trick but solves an annoying problem for those of us who use our
Androids as a media center. To use it, just tap the button to
turn off your backlight and you're set. You can still see the
image you're streaming on your TV (or wherever), but your screen
will be off. To get things back to normal, all you have to do is
lock and unlock your device.  Screen Standby is free to
download, but it does require rooting your device.  Screen
Standby | XDA Developers