We should be able to safely rule out E based on the awkawardness of the structure, so let's go to A-D.

A: "when a child" is improper because we're referring to patients, which is plural, so patients at large were never "a child"

B: when children....what? here, children could be the subject of an incomplete phrase, but we can't have the phrase be "contracted when children." however, this should be a hint: the reason this answer is put here is because it *sounds* correct because, as we know, the correct answer is D. in ordinary usage, someone might say "when children," but we're looking for gramatical preciseness here.

C: "that was" is superfluous and "when a child" suffers the same problem as in A

D: bingo. when did the patients contract polio? "when they were children." the patients did not contract polio when they were a child. see how much clearer it is when you structure it as such?

Studies conducted in the 1990s indicate that even after fifty years, patients are still suffering the long term effects of polio occurring when a child.

A. contracted when a child (awkward, and doesn't work with plural "patients")
B. contracted when children (awkward)
C. that was contracted when a child (same problem as A)
D. contracted when they were children (good)
E. that has been contracted as each was a child (it is incorrect to use present perfect for an event that occurred fifty years ago)

On an unrelated note, Ludacrispat26 I love your avatar! I never should have given up animation rights...

Thanks Ludacrispat26 & Bill@VeritasPrep..