The Wife cannot be taken back after the Third Divorce
[فَإِن طَلَّقَهَا فَلاَ تَحِلُّ لَهُ مِن بَعْدُ حَتَّى تَنْكِحَ زَوْجًا غَيْرَهُ]
(And if he has divorced her (the third time), then she is not lawful for him thereafter until she has married another husband.)
This Ayah indicates that if the man divorces his wife for the third time after he divorced her twice, then she will no longer be allowed for marriage to him. Allah said:
[حَتَّى تَنْكِحَ زَوْجًا غَيْرَهُ]
(...until she has married another husband.) meaning, until she legally marries another man. For instance, if she has sexual intercourse with any man, even her master (if she was a servant), she would still be ineligible for marriage for her ex-husband (who divorced her thrice), because whomever she had sexual relations with was not her legal husband. If she marries a man without consummating the marriage, she will not be eligible for her ex-husband. Muslim reported that `A'ishah said that Allah's Messenger was asked about a woman who marries a man who thereafter divorces her (thrice). She then marries another man and he divorces her before he has sexual relations with her, would she be allowed for her first husband Allah's Messenger said:
«لَا، حَتَّى يَذُوقَ عُسَيْلَتَهَا»
(No, until he enjoys her `Usaylah (sexual relation).) Al-Bukhari also reported this Hadith.
Imam Ahmad recorded that `A'ishah said, "The wife of Rifa`ah Al-Qurazi came while I and Abu Bakr were with the Prophet and she said, `I was Rifa`ah's wife, but he divorced me and it was an irrevocable divorce. Then I married `Abdur-Rahman bin Az-Zubayr, but his sexual organ is minute like a string.' She then took a small string of her garment (to resemble how small his sexual organ was). Khalid bin Sa`id bin Al-`As, who was next to the door and was not yet allowed in, said, `O Abu Bakr! Why do you not forbid this (woman) from what she is revealing frankly before the Prophet' The Prophet merely smiled. Then, Allah's Messenger asked her: c
«كَأَنَّكِ تُرِيدِينَ أَنْ تَرْجِعِي إِلى رِفَاعَةَ، لَا، حَتَّى تَذُوقِي عُسَيْلَتَهُ، وَيَذُوقَ عُسَيْلَتَك»
(Do you want to remarry Rifa`ah You cannot unless you experience his `Usaylah and he experiences your `Usaylah (i.e., had a complete sexual relation with your present husband).)''
Al-Bukhari, Muslim, and An-Nasa'i also recorded this Hadith. Muslim's wording is "Rifa`ah divorced his wife for the third and final time."
The word `Usaylah mentioned in the Hadith means sexual intercourse. Imam Ahmad and An-Nasa'i reported that `A'ishah said that Allah's Messenger said:
«أَلَا إِنَّ الْعُسَيْلَةَ الْجِمَاع»
(`Usaylah is sexual intercourse.)