What happens in the case of split votes with an even number of board members present?
Essentially in the case of a tie nothing happens - it is as if there was no motion and vote taken. Sometimes it is easier if we have a specific example...
Let's say the superintendent/president/chief exec asks the board to approve a new program. The motion is to approve the program and it ties 3-3. So there is no approval - but it isn't denied either - the result is as if the board has taken no action.
Then there is a motion to deny the program. The vote again ties. The program is not denied - neither is it approved. It is as if the board never took up the issue.
An example occurred recently when the superintendent decided not to offer a coach a new contract for the next year. This was within the superintendent's duties, and did not require board approval. The board heard an appeal from the coach to over-ride the superintendent's decision. They split 3-3 on a motion to over-ride the superintendent's decision. Since the vote failed the superintendent's decision stood. The Board members went away and thought about it, came back the next week and tried a motion to support the superintendent's decision. It tied 3-3. The side that wanted his decision overturned argued that this meant his decision was overturned because the motion of support failed. Not true. It was simply that no action was taken - as if the board had never taken up the issue. The superintendent's decision continued to stand.
The topic may be brought up again at another meeting with no steps taken regarding reconsideration. Reconsideration is complicated and is used when a motion has passed or failed and then the board wants to re-vote it, generally at the SAME meeting. There are some technical rules we can get into for reconsideration if a follow up motion and vote is taken to restrict reconsideration but that is beyond your question. Also reconsideration is restricted if the result of the first vote is contractually binding action by the organization. Again......beyond the question.
Your tied motion can continue to be taken up again and again at the SAME meeting with no need to do anything about reconsideration because no successful vote was made and no action taken. However a smart chair will suggest putting a limit on that in the interest of time and frustration.