Just because our consciousness is not active at that time doesn't mean our brains aren't receiving input and processing it. Have you never, for instance, had a dream in which you felt very cold, and then woke to find that you had kicked the blankets off?
In any case, the point isn't that the continuity of input must be absolutely constant from "birth" to "death"; is that the input must be continuous as opposed to discrete. I could easily imagine an advanced, conscious AI that was "put to sleep" repeatedly to adjust things that can't be (easily? safely?) adjusted while it's "conscious", and that "sleep" would be much more comprehensively "offline" than our own. But the AI itself could still be reasonably considered "conscious" despite those periods, because during the rest of the time, its input is continuous. (Plus the other requirements, however nebulous and unknown they may be now.)
In any case, the point isn't that the continuity of input must be absolutely constant from "birth" to "death"; is that the input must be continuous as opposed to discrete. I could easily imagine an advanced, conscious AI that was "put to sleep" repeatedly to adjust things that can't be (easily? safely?) adjusted while it's "conscious", and that "sleep" would be much more comprehensively "offline" than our own. But the AI itself could still be reasonably considered "conscious" despite those periods, because during the rest of the time, its input is continuous. (Plus the other requirements, however nebulous and unknown they may be now.)