Praise be to Allah.
When a husband deprives his wife of the right to intercourse, the scholars call this eelaa’. Eelaa’ means the vow of the husband who is able to have intercourse never to have intercourse with his wife, or not to have intercourse with her for more than four months. The evidence for that is the aayah (interpretation of the meaning):
“Those who take an oath not to have sexual relation with their wives must wait for four months, then if they return (change their idea in this period), verily, Allaah is Oft-Forgiving, Most Merciful[al-Baqarah 2:226]
It was narrated that Ibn ‘Umar (may Allaah be pleased with him) used to say concerning eelaa’: “If the period of eelaa’ expires, then the husband has either to retain his wife in a handsome manner or to divorce her as Allaah has ordered” (al-Bukhaari, al-Talaaq, 4881)
Eelaa’ is forbidden in Islam because it is a vow not to do something that is obligatory. It is in effect a vow not to have intercourse with one's wife, either never again or for a period that exceeds four months; or else it means vowing that if one’s wife does not do a certain obligatory action or does a certain haraam action, he will not have intercourse with her. The fuqahaa’ also said that the one who does not have intercourse with his wife for more than four months without swearing an oath, in order to harm her and without having a valid excuse, also comes under the category of eelaa’.
The ruling on this matter is: that if he has intercourse with his wife during that period, then he has “returned”, because “returning” in this context means intercourse and in this manner the woman has attained what she is entitled to from him. If he refuses to have intercourse after the stated time limit has expired, then the judge should order him to divorce her if his wife requests that. If he refuses to have intercourse and he refuses to divorce her, then the judge should issue a divorce and annul the marriage.
And Allaah knows best.
For more information refer to Zaad al-Ma’aad by Ibn al-Qayyim, vol. 5/344
If it is the case that the husband is sick, please see Question No 1859, 5684