"Vertically challenged" is an interesting phrase only because of the "challenge" part. Challenged by what? Genetics? Nobody says a dark skinned person is "shade challenged" or whatever else.
The best anyone could come up with is that short people struggle to reach things. Clearly baloney as the average woman would be considered vertically challenged if this were the case. Even
though a typical short man can reach the same things as her, since he's below the
average male height he's "vertically challenged." Extremely tall people tend to complain about physical problems like hitting their heads but they're not considered challenged either.
Unfortunately I couldn't find any fun facts on the origins of this line, unlike "bottom of the totem pole."