Great demo, AIM GMAT - to answer Prachich's question, the "that" is actually required to make that section of the sentence parallel. Answering even further, "that" after a comma works in this case because the commas around:
..., despite the recent illnesses, ....
contain a nonessential modifier. When you see a modifying phrase bracketed by commas, the commas serve as a way to make that modifier "easily removable", like a temporary extension to a dinner table for when company comes (if any of you had that growing up...I remember helping my mom extend the table for Thanksgiving every year). The GMAT loves to extend sentences with nonessential modifiers because it distracts the reader from big-picture errors like subject/verb agreement or, in this case, parallelism. So as a strategic point, when you see those commas separating out nonessential modifiers, try reading the sentence as though that portion isn't there, and you'll typically make your job easier.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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