The screen shouldn't be damaged if kept on (I've kept mine on for more than 2 days without issues). Unfortunately, iRex has not yet implemented a suspend-to-flash feature like (yet) the Sony has, so there is no way to "push a button" and put the device to sleep.
If you are not using the device for 2-3 hours, you might want to shut it down to conserve battery. This is the only way to turn the screen off right now, although you have to go through the longish boot up time later (and have to re-open your old documents).
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