Is it permissible to persist in shunning one's wife who apostatized after an argument, then repented and sought forgiveness, knowing that she has repeated this act before?

If the wife utters words of disbelief (kufr) unintentionally, she is not considered a disbeliever, because accountability is for intentional actions. It is not permissible for a Muslim to remain with his wife if she apostatizes from Islam. The Hanafis, Malikis, and Hanbalis (in one narration) hold that the marital bond ceases immediately upon the wife's apostasy. However, the Shafi'is and Hanbalis (in another narration, which is the stronger opinion) hold that separation is contingent upon the expiry of the waiting period ('iddah) before her repentance. If she repents before the 'iddah expires, the marriage remains valid. As long as the wife did not commit disbelief with what she uttered unintentionally, or if she repented before her 'iddah ended, she remains his wife. It is obligatory to deter her from repeating such actions, to explain their danger, and to teach her matters of her religion and assist her in acts of obedience.