Praise be to Allah.
Prayer is very important and it is the most essential of the pillars of Islam after the Shahadatayn (testimonies of faith). It is the foundation of Islam and the one who does not pray has no share of Islam, as ‘Umar (may Allah be pleased with him) said. There is a great deal of evidence which indicates that not praying is tantamount to kufr which puts one beyond the pale of Islam. Please see the answer to question no. 5208.
If a person loves his Lord and he loves His Prophet and His religion and His Book, then how can he waste the greatest opportunity that he has been given, even though it is an easy and pleasant obligation, which brings ease to the heart, contentment to the soul and purity to the body. Those who neglect the prayer and delay it until after its time are also given a warning of punishment, as Allah says (interpretation of the meaning):
“Then, there has succeeded them a posterity who have given up As‑Salah (the prayers) [i.e. made their Salah (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 Allah be upon him) said: “The one who does not pray ‘Asr, his good deeds will bear no fruits.” Narrated by al-Bukhari (553).
What you have to do is continue advising your wife, and be strict with her with regard to prayer, and check on her with regard to every prayer until she is praying regularly. Beware of missing any prayer until the time for it is over.
You should inform her of the ruling on one who does not pray, and of the scholarly view which says that the one who misses a single prayer until the time for it ends with no excuse is a kafir, and the resulting invalidity of the marriage according to some fuqaha, so that this will be a rebuke that will scare her.
Allah 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, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allah, but do that which they are commanded”
And the Prophet (peace and blessings of Allah be upon him) said: “A man is the shepherd of his household and is responsible for his flock.” Narrated by al-Bukhari (893) and Muslim (1829).
Try to encourage and warn her with all possible means, but let your advice to her be given kindly and gently, because there is no kindness in a thing but it adorns it. Reward her and encourage her if she prays, and remind her that prayer is the key to happiness and divine help, and is one of the causes of abundant provision and a happy life. If that produces results, and leads to her praying regularly, that is what is required and it is what we hope and want for her. But if she persists in falling short, then there is no reason why you should not resort to stricter means such as denouncing her sometimes, according to whatever will serve the interest.
He was harsh so that they might pay heed; a man of resolve may be harsh sometimes with those whom he loves.
So forsake her and threaten her with divorce, so that she will realize that the matter is serious, and she will realize that you cannot live with a woman who neglects the most important duty of Islam, no matter how obedient and hard-working she is with regard to worldly matters.
The aim behind all of that is to set her straight, hence we advise you to be patient with her and not to lose hope. Allah says (interpretation of the meaning): “And enjoin As‑Salah (the prayer) on your family, and be patient in offering them [i.e. the Salah (prayers)]” [Ta-Ha 20:132].
Engage in a lot of du’a asking Allah to guide your wife and set her straight.
And Allah knows best.