“... somebody on the winning side of the cloture vote — in this case, the side voting against cloture — has to file a “motion to reconsider” if the matter is to be taken up again... any supporter of the bill or nomination in question could do the same, but traditionally it’s been the majority leader.”
That’s why! The cloture motion can be reconsidered ad infinitum but it can only be brought up by a ‘winner’ of the cloture vote.
I agree wuth that, just saying that a failed cloture motion doesn't preclude filing a second, third, fourth, fifth, ad infinitum cloture votes on the same subject. Multiple cloture motions is (or at least used to be) the common method of having "the same" (cloture) vote multiple times.