Screen going idle during streaming video

What video player are you using? Some players support disabling screensavers or certain ACPI events when video is playing. I believe VLC can do this.

Is a known behaviour (not a bug) as shown here http://forum.videolan.org/viewtopic.php?f=13&t=68419

See the last comment about using the "Inhibit Applet" that allows you to disable/modify (temporarily) the power settings.

1. Right click on the panel (bar on top of the screen)
2. select "add to panel
3. search for "inhibit"
4. click ok

When starting to watch the movie, click on the icon

the previous two answers are assuming that you use VLC, is that what you actually use?
other than that, did you check the screensaver setting or if the monitor has some automatic dimming of its own?
did you try other things, like watching a YouTube video longer than 15 minutes or maybe using other video players?

To build on pmarini's response, it sounds like a power management setting.

You can change it so that your monitor isn't turned off x number of minutes.

System -> Preferences -> Power Management

Change the setting to never set display to sleep.

look at "caffeine". It will do what you want.

You can read all about it at:

https://launchpad.net/~caffeine-developers/+archive/ppa

For Ubuntu, Installing it is just a matter of adding the appropriate archive to your repositories list. You can do that a couple of ways. For a step-by-step, look at:

http://tuxtweaks.com/2010/07/keep-your-screen-awake-with-caffeine/

Good Luck.