because, by the explicit text of the Quran, a disbeliever may not marry a Muslim woman. Whether one who abandons the prayer is deemed a disbeliever or not is another matter.
But if we judge him to be a disbeliever—and that is the stronger view—then, by the explicit text of the Quran, the marriage is invalid.
If, at the time of the contract, he used to pray but later ceased praying, then if this occurs before consummation, the marriage is dissolved and she may marry immediately. If it occurs after consummation, the marriage is dissolved, but she must wait until the waiting period has ended. If Allah guides him back to Islam, he remains her husband; otherwise, she may marry.
Many women—may Allah protect us—are prevented by the presence of children from seeking dissolution of the marriage. This is a serious matter. It should be said to her: “Seek dissolution of the marriage. You must not remain with this disbeliever who does not pray. Your children will not be taken away from you so long as their father remains in this state, for he has no legal guardianship over them. A disbeliever has no authority over a believer: ‘And never will Allah give the disbelievers a way over the believers.’” [Surah al-Nisa 4:141]
He will not separate you from your children. As for this husband, there is no good in him: a disbelieving husband whom you allow to make lawful with you what is forbidden! This is a grave evil.