His wife does not pray regularly
What the husband should do is enjoin good upon his wife and forbid her to do that which is evil. He should call her to do good and warn her against evil, thus fulfilling the responsibility that Allaah has given him. Allaah says (interpretation of the meaning):
“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones”
And the Prophet (peace and blessings of Allaah be upon him) said: “A man is the shepherd of his household and is responsible for his flock.” Narrated by al-Bukhaari (893) and Muslim (182).
One of the greatest of good deeds is performing prayer on time as enjoined by Allaah, and one of the greatest of bad deeds is being careless and negligent about that, by not praying at all, or by not praying on time. Allaah criticized the one who does that, as He says (interpretation of the meaning):
“Then, there has succeeded them a posterity who have given up As‑Salaah (the prayers) [i.e. made their Salaah (prayers) to be lost, either by not offering them or by not offering them perfectly or by not offering them in their proper fixed times] and have followed lusts. So they will be thrown in Hell”
And the Prophet (peace and blessings of Allaah be upon him) said: “Between a man and shirk and kufr there stands his giving up prayer.” Narrated by Muslim (82).
And he (peace and blessings of Allaah be upon him) said: “The one who does not pray ‘Asr, his good deeds are fruitless.” Narrated by al-Bukhaari (553).
If your wife does not pray at all, then there are ahaadeeth from the Prophet (peace and blessings of Allaah be upon him) which show that not praying at all is kufr, and it is not permissible for you to keep her because she is not a Muslim. In that case you have to tell her that her insisting on not praying means that she is not your wife, so she must either repent and start to pray regularly, or else you must leave her.
But if she prays sometimes and not at others – which seems to be the case from your question – then that does not put her beyond the pale of Islam, but you have to advise her and look for the causes of her shortcoming so that they can be dealt with. But that should be done in a kind and gentle manner. So explain to her the importance of prayer, and the sin involved in falling short with regard to it. Strive to strengthen her faith and encourage her to do good deeds and acts of worship. Help her to make friends with some righteous women and supply her with some useful books and tapes that will encourage her to do good, and always ask her about her prayers.
We ask Allaah to guide you both to that which is good.
See also question no. 12828.
And Allaah knows best.