It is permissible for a sick person to join prayers, so he may join Zuhr and ‘Asr, or Maghrib and ‘Isha’, at the time of the earlier or later prayer, depending on what is easiest for him.
Difficulty caused by sickness is one of the excuses which make it permissible to join prayers. The Prophet (peace and blessings of Allaah be upon him) granted a concession to the woman who suffered from istihaadah (non-menstrual bleeding), and he allowed her to join prayers.
(Abu Dawoud, 287; al-Tirmidhi, 128).
Istihaadah is a kind of sickness, and Imam Ahmad quoted as evidence for it being permissible for a sick person to join prayers the fact that sickness is worse than travel. He was treated with cupping after sunset, then he ate supper then he joined Maghrib and ‘Isha’ prayers.
(Kashshaaf al-Qinaa’, 2/5).
It should be noted that the sick person for whom it is permissible to join prayers should offer each prayer in full without shortening it, because shortening of the prayers is only permitted for the traveller. What some people think, that if a person joins the prayers at home because of sickness he is also allowed to shorten them, is not correct.
And Allah knows best.
23 Jumada Ula, 1442 AH.
