The losing side in a failed cloture vote may, but need not have one member switch sides in order to make a motion to reconsider. I've always found the motion to reconsider a failed cloture vote to be moronic. There is no rule that says cloture can be called for only once on a given point. The Republicans made 8 cloture motions (6 failed votes, the 7th and 8th motions were withdrawn) to limit debate on a Motion to Proceed to the Consideration of a bill authorizing funds for the investigation of the Whitewater Development Corporation.
See Examples of cloture on "motion to proceed" (links to Congressional Record). If a cloture motion fails, just file another one. All Reid is doing with his "motion to reconsider" is protecting a sophomoric "number of times the other party made a cloture motion" sort of statistic. I see no purpose even for that.
I have no idea why it’s done that way, but we’ve seen it many times over the past 8 or 12 years.
“It’s just the way it is.”
;-)