Praise be to Allah.
It should be known that the one who does not pray any of the prayers and persists in not doing so, according to the Sahaabah and the majority of scholars, is counted as a kaafir and it is not permissible to marry him or eat meat slaughtered by him. If the husband does not pray at all, then he is taking a very serious risk and it is not permissible for you to stay with him. You have to remind him and scare him with this. Withholding yourself from having intercourse with him is the right thing to do, until he starts to pray, because the one who does not pray is counted as a kaafir, as it was reported in Saheeh Muslim from the hadeeth of Jaabir that the Prophet (peace and blessings of Allaah be upon him) said:
All that stands between a man and shirk and kufr is his giving up prayer. And he also said:
The covenant that separates us from them is salaah, and whoever gives up prayer is a kaafir.
Abd-Allaah ibn Shaqeeq said: the companions of the Prophet (peace and blessings of Allaah be upon him) used not to count the giving up of any action as kufr, apart from prayer. You have to warn your husband against neglecting the prayer. If he persists, it is not permissible for you to stay with him because you are a Muslim and he is something else. May Allaah help the Muslims to do what Allaah has commanded and to obey Him. You have to advise and scare him, and may Allaah bring about good for him through that.