Answer: It's not really all flats coming down.

Start with the natural minor - that's the pattern of the white keys if you play from from A to A on the piano. And of course thay same pattern of steps can be played starting on any note - like D natural minor, which is D, E, F, G, A, Bb, C, D.

When a minor melody is upward-bound, the 7th degree is often raised a half step so that it will make a "leading tone" to the tonic. So in the scale on A that would be G# instead of G. That's "harmonic minor," because this change to G was made for harmonic purposes.

But if the A minor melody had an F before the G it might be good to raise the F, too, if the composer wants to avoid the exotic-sounding augmented second of F to G#. So then the F gets raised as well, and you end up with a minor scale from A that reads: A, B, C, D, E, F#, G#, A. We call that "melodic minor," presumably because the change was made for melodic reasons.

On the way down, a melody isn't going to need that raised 7th degree because it's not leading to the tonic - so the G can be used without alteration. And if the G isn't changed there's no reason to change the F, either. So really the A minor scale coming downward is going to be the plain natural minor: A, G, F, E, D, C, B, A.

By long custom in music school, we say that the "melodic minor" has two forms, ascending and descending. But really the minor scale is a variable one whose 6th and 7th degrees are often altered, particularly when ascending. A descending "melodic minor" is just the natural minor scale again. See also question 87.