All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
When the husband repudiates his wife for the third time, it triggers a "major" divorce {Talaq Ba`in Bainonah Kubra}. Thus, she has to marry another man, consummate the marriage with him and get divorced again in order to be able to marry her former husband. This is of course after she finishes her Iddah, which is, in this case, three months. The evidence on this is that Allah the Almighty Says {What means}: "So if a husband divorces his wife (irrevocably), He cannot, after that, re- marry her until after she has married another husband and He has divorced her. In that case there is no blame on either of them if they re-unite, provided they feel that they can keep the limits ordained by God. Such are the limits ordained by God, which He makes plain to those who understand." {Al-Baqarah, 230}.
`Aisha narrated: The wife of Rifa`a Al-Qurazi came to Allah's Messenger (PBUH) and said: "O Allah's Messenger (PBUH)! Rifa`a divorced me irrevocably. After him I married `Abdur-Rahman bin Az-Zubair Al-Qurazi who proved to be impotent." Allah's Messenger (PBUH) said to her: "Perhaps you want to return to Rifa`a? Nay (you cannot return to Rifa`a) until you and `Abdur-Rahman consummate your marriage." {Related by Bukhari}.
However, if the second husband doesn`t consummate the marriage with the woman who had received a "major" divorce from her first husband, then it is unlawful for her to return to the latter. This is reflected in Article (95) of the Jordanian Personal Status Law, which states: "The woman who had received a "major" divorce from her first husband isn`t allowed to return to him unless she marries another man, consummates the marriage and gets divorced." Accordingly, the above woman (Asker) isn`t allowed to return to her former husband because she didn`t consummate the marriage with her second husband. And Allah the Almighty Knows Best.