This is a complete-the-passage item. The connector "because" signals that the blank must supply the reason that makes the administrators' conclusion follow from the evidence. The evidence: total weekly borrowing held steady after Brightwood cut its Sunday hours. The conclusion: the patrons who had previously borrowed on Sundays did not simply stop borrowing. The gap is that a steady total is consistent with the Sunday borrowers dropping out if some other group of patrons increased its borrowing by exactly enough to offset the loss. To force the conclusion, the completion must rule out that offsetting increase.
Think of the weekly total as two parts: borrowing by patrons who used to borrow on Sundays, plus borrowing by patrons who never did. The total is unchanged. (C) tells us the second part, the never-on-Sunday patrons, did not change how much they borrowed. If that part stayed flat and the whole stayed flat, the first part, the former Sunday borrowers, must also have stayed flat, so they did not stop borrowing. (C) is exactly what closes the gap, and no other completion makes the conclusion follow.
Why each other choice fails: (A) brings in circulation at libraries in neighboring towns, a different population of patrons entirely; a rise elsewhere does not show that Brightwood's own former Sunday borrowers kept borrowing. (B) shows only that Sunday items were also available on other days, which makes a shift in borrowing possible, but it does not establish that the former Sunday patrons actually kept borrowing; the steady total is still equally consistent with them dropping out while some other group takes up the slack. (D) runs the wrong direction: if patrons strongly preferred visiting on weekends, removing Sunday hours would more likely have driven those patrons away, which works against the conclusion rather than for it. (E) adds a detail about when the library decided to cut weekend staff, which says nothing about whether the former Sunday borrowers kept borrowing items, so it addresses a different link than the one the conclusion turns on.
The answer is (C).