That's a very good question:

Normally, I simply leave it on at all times, and I have zero problems getting it to operate properly the next day. My Boxee Box has been powered on since the last update...

...and that's because I have to restart in order to update. So far, every time an update has come through, it has shown a notification (as you might expect), and I don't know if the problem is that I don't react to the notification for a long while or not, but for whatever reason I'm unable to do ANYthing. I can't move the cursor around, I can't select anything, and nothing I hit on the remote causes anything to happen on the screen. From what I recall, even the options I'm given are a little messed up, where one button doesn't have text in it or something.

But in the end, this isn't a big deal, as simply tapping the power button on the Box its self and tapping it again to turn it back on fixes the problem and I can update manually. And like I said, the rest of the time I simply leave it turned on, logged in, and not in standby (though it does go into its screensaver mode, of course).
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Matt