Tie votes

A tie fails, it does not pass

A motion needs a majority, more than half of the votes actually cast, to pass. A tie is exactly half. Half is not more than half, so the motion is lost, the same as if it had lost outright. There is no rule that treats a tie as a pass by default, and no rule that automatically sends it to a revote at the same meeting.

"On a tie vote the motion is lost, and the chair, if a member of the assembly, may vote to make it a tie unless the vote is by ballot."

Source: Robert's Rules of Order, Henry M. Robert (1915 edition, public domain)

What the board president can actually do

A common belief is that the board president only votes to break a tie. That is not quite right. If the president is a voting member of the board, they have exactly the same right to vote on every motion as any other director, first or last. The narrower, real rule is about timing: on a vote that is not by ballot, the president may hold back and let the count fall where it does, then step in with a vote at the point where it would create or break a tie.

"If the president is a member of the voting body, he or she has exactly the same rights and privileges as all other members have."

Source: Robert's Rules of Order Newly Revised, Frequently Asked Questions, Robert's Rules Association

That option does not carry over to a secret ballot vote the same way, since a ballot is not tied to a visible, running tally the way a voice or show of hands vote is. Whether your board even uses ballot votes for ordinary motions, and how ties are handled if it does, is worth confirming against your own bylaws.

Reconsidering a tied vote

A tie means nothing was adopted, so there is nothing on the books to rescind or amend, those tools exist for actions the board already approved. What is available is the motion to reconsider, and it comes with real limits. It must be made at the same meeting the tie happened at (or the next day, if the meeting runs more than one day), and only a director who voted with the side that defeated the motion, here, someone who voted no, may make it. Reconsideration itself then needs its own majority vote before the original question is even reopened.

"If the Motion to Reconsider passes, then the body takes up the original motion as it was just before the vote was taken."

Source: Changing Course: Using Robert's Rules to Alter a Prior Action, MRSC

If that window has already closed, ask whoever chairs your meetings, or check your bylaws' named parliamentary authority, about whether the same proposal can come back as a brand new motion at a future meeting.