After a day devoid of alien, the process of creating a new one would need to start from scratch.
And that means evolving the alien from a few cells (yes, those are supposed to be cells, not floating eyeballs) in some primordial ooze. Fortunately, our time-traveling mascot will be able to expedite this process so it only takes a week. I understand such things normally take much longer.
Cells are dividing. See, Ellen (evolutionary biology PhD student) I'm finally doing that alien evolution series you suggested so long ago. I just couldn't wait until Darwin's birthday. The next few days could get interesting; natural selection isn't always pretty. I thought it'd be best to explain before the logos got even weirder.
I wasn't kidding when I said this would be an epic doodle series, Homer wishes he could see this -- well, he'd probably wish he could see.