The reason for repeating the divorce statement thrice is due...

The reason for repeating the divorce statement thrice is due to the time interval between each, and due to a possible desire for reconciliation or the calming of anger, if any, and to teach women to fear their husbands and deter them from disobeying them.

The reason why a husband can never remarry his wife whom he divorced thrice (articulating, in the process, the divorce statement nine times all in all), is that it is his right penalty so that men do not take divorce lightly or take advantage of women and think of them as weak, and so that the man would be considering his affairs, remaining awake and aware, so that he would lose all hope of a reunion after the ninth pronouncement of the divorce statement.

The reason why a wife during her waiting period ( 'iddat ) cannot remarry her previous husband who had divorced her twice before till she marries someone else, is due to the fact that God had permitted divorce twice, saying, "A divorce is only permissible twice: after that, the parties should either hold together on equitable terms, or…