Well, it's a parliamentary question here. In Robert's Rules, any motion may be reconsidered by a member who voted with the prevailing side. However, since the vote was viva voce, we have to take on faith that the motion maker voted with the prevailing side on the nominaiton.

In general, the motion to reconsider can be made only on the same day, or on the next legislative day.

However, it is also general parliamentary practice that it is not in order to re-consider an affirmative vote of a motion to "elect to membership or office if the member or officer is present and does not decline, or if absent and has learned of his election in the usual way and has not declined."

Also, there being concern that the motion had not obtained two-thirds. If a point of order is raised later that the motion had not obtained two-thirds to agree to the nomination, the point of order should be held out of order as untimely. If there is a question as to whether a voice vote has achieved the necessary majority, a call for division should be requested at the time of the vote before the chair finalizes the vote with "I think the AYEs have it and the AYEs have it."

However, I'm not sure which parliamentary manual is used by the ASUC, and any by-law or article of the constitution overrides any portion of a parliamentary manual. But you knew that.
 

The ASUC Senate uses Robert's Rules. The question of whether or not the person received two thirds was raised by an observer (me), so obviously there was no call for division.

That said, there is a viewpoint that, in an externally regulated representative Senate, the rules of order that limit the ability to check rule compliance to the Senate itself are invalid. This is also supported by the ASUC Constitution in denying the Senate the ability to suspend the By-Laws, even by unanimous consent, without one week notice.

This sequence of events is fairly interesting, because I don't think there's a consistent interpretation of the By-Laws which allows it.