As others have already said (just adding my agreement), it's a known problem. Sometimes it will look like it shutdown (screen is blank, etc), but there is still something "stuck" running on the device. That'll cause it to drain the battery overnight. General tips are to close any documents (some have said that removing the SD card helps to) before shutting it down.
Another thing to watch for is that the red LED means there was an error, but there is usually also a combination of green LEDs that come on too. The specific green LEDs that come on give you more information about what the exact error was. We're still trying to find out more details on what different combinations mean, but one we do know is that the red LED plus the lower two green LEDs on the right hand side means "Battery power too low for startup".
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