Islam discourages Muslims from going back and forth about their decisions, engaging in emotional blackmail, or leaving the other spouse in limbo. The Quran says, "When you divorce women and they fulfill the term of their iddat, either take them back on equitable terms or set them free on equitable terms; but do not take them back to injure them, (or) to take undue advantage. If anyone does that, he wrongs his own soul..." (Quran 2:231) Thus, the Quran encourages a divorced couple to treat each other amicably, and to sever ties neatly and firmly.
If a couple decides to reconcile, after the divorce is finalized, they must start over with a new contract and a new dowry (mahr). To prevent damaging yo-yo relationships, there is a limit on how many times the same couple may marry and divorce. If a couple decides to remarry after a divorce, this can only be done twice. The Quran says, "Divorce is to be given two times, and then (a woman) must be retained in good manner or released gracefully.” (Quran 2:229)
After divorcing and remarrying twice, if the couple then decides to divorce again, it is clear that there is a major problem in the relationship! Therefore in Islam, after the third divorce, the couple may not remarry again. First the woman must seek fulfillment in marriage to a different man. Only after she is divorced or widowed from this second marriage partner, would it be possible for her to reconcile again with her first husband if they choose.
This may seem like a strange rule, but it serves two main purposes. First, the first husband is less likely to initiate a third divorce in a frivolous manner, knowing that the decision is irrevocable. One will act with more careful consideration. Secondly, it may be that the two individuals were simply not a good match for each other. The wife may find happiness in a different marriage. Or she may realize, after experiencing marriage with someone else, that she wishes to reconcile with her first husband after all.