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In many other contexts, "falling down" would be ok. But as has been pointed out obliquely, "The sky is falling!" is an idiomatic phrase in English, coming from a nursery rhyme/folk tale about a chicken named "Chicken Little" or "Chicken Licken" or "Henny Penny". That's why an English speaker would never say "The sky is falling down, because in the story, Chicken Little always said "the sky is falling!"
I would say that the verb "to fall down" is a different verb to simply "to fall". "To fall" is simply to act under the influence of earth's gravity. "To fall down" is to fall due to a system failure: a house can fall down if poorly built; a pair of trousers can fall down if the support fails; but the word "down" is superfluous for an item falling from an aeroplane.
This sentence belongs to the Pearson part of the course (see https://www.duolingo.com/comment/24066422 if you haven't heard about their influence on the course).
I haven't seen anything so far to indicate that they act on reports or read sentence discussions, but by all means, keep reporting.