Prayer is the main pillar of faith and the main article of Iman. A Muslim is asked to perform it in all cases. If one cannot do it while standing, then he can do it while sitting or while lying in his bed.
In the light of the above, it is crystal clear that “Prayer is the only pillar in Islam that cannot be waived under any circumstances, unless a person is mentally handicapped. It has to be performed, whether a person is traveling, sick, poor, rich, married, pregnant, old, etc., unlike other pillars (fasting, pilgrimage, and Zakah, that can be waived under certain conditions. There is no provision in Islam to miss any prayers, unlike other pillars such as fasting or paying Zakah, or performing pilgrimage which can be missed but made up later only under special circumstances (such as being poor or sick or traveling, etc.) and if there is the ability to do so. Even if you are sick and are lying on a bed in a hospital without being able to move, you have to pray with your eyes. This shows how essential prayer is and how no one is allowed to downplay its importance.” (Excerpted, with slight modifications, from: www.islamicity.com)
Addressing the issue of making up for missed prayer, Sheikh Muhammad Salih Al-Munajjid, a prominent Saudi scholar and author, states the following: “When a person misses a prayer unintentionally, this may happen due to a legitimate excuse, such as forgetting or sleeping, although he is basically very keen to perform the prayer on time. In this case one is excused but he is to make it up as soon as he remembers it. When the Prophet (peace and blessings of Allah be upon him) and his Companions slept and missed Fajr prayer, and the Companions began to ask one another: “What is the kaffarah (expiation) for what we have done by neglecting the prayer?” The Messenger of Allah (peace and blessings of Allah be upon him) said: “Sleeping does not mean that you are neglecting the prayer. Rather neglecting the prayer means not praying one prayer until the time for the next prayer comes. Whoever does that let him pray when he remembers it.”
In case a person misses a prayer deliberately, this is a major sin, and it is so serious that some of the scholars stated that the one who does this is a kafir (as it says in Majmu` Fatawa wa Maqalat Samahat Ash-Sheikh Ibn Baz, 10/374). The one who does this has to repent sincerely, according to scholarly consensus. With regard to making up the prayer, there was a difference of opinion among the scholars as to whether or not it would be accepted from him if he makes it up afterwards. Most of the scholars said that he should make it up and that his prayer is valid, although he is a sinner (i.e., if he does not repent – and Allah knows best), as Sheikh Ibn `Uthyameen quoted from them in Ash-Sharhul-Mumti’, 2/89. The view chosen by Sheikh al-Islam Ibn Taymiyah (may Allah bless his soul) is that it is not valid, and that it is not prescribed for him to make it up. He said in Al-Ikhtiyarat (34): “It is not prescribed for the one who misses a prayer deliberately to make it up, and the prayer, if he makes it up, is not valid; rather he should do a lot of nafl (voluntary) prayers. This is the view of a group among the Salaf.” One of the contemporary scholars who regarded this view as more correct is Sheikh Ibn ‘Uthaymeen (may Allah bless his soul); he quoted as evidence for that the words of the Prophet (peace and blessings be upon him): “Whoever does an action that is not in accordance with this matter of ours (i.e., Islam), will have it rejected.” (Agreed upon). So, one must beware of this and strive to perform all the prayers on time, as Allah says: “Verily, prayer is enjoined on the believers at fixed hours.” (An-Nisa: 103)”
Almighty Allah knows best.