Ruling on a doctor who misses the prayer because he is busy with surgery
Question

                There is a doctor who does emergency surgery, which sometimes means that he is too busy to pray until the time of the prayer ends. What should he do? He has been told that in that situation he must offer the prayer in any way. What is this way? May Allah reward you.
Praise be to Allah.
      What the Muslim is obliged to do is to offer the prayer on 
      time and not let himself be distracted from it by anything, unless it is 
      something urgent that he cannot do anything about, such as saving a person 
      from drowning or rescuing people from a burning house, or warding off the 
      attack of an enemy that is feared. In such cases there is nothing wrong 
      with delaying the prayer for that reason, even if the time for the prayer 
      ends. But with regard to ordinary matters in which no danger is involved, 
      it is not permissible to delay the prayer because of them. 

    It is proven that the Prophet (blessings and peace of Allah 
    be upon him), when the people of Makkah besieged Madeenah on the day of al-Ahzaab, 
    delayed Zuhr and ‘Asr prayer until after Maghrib. According to another 
    report, he delayed ‘Asr prayer until after Maghrib, because he was 
    preoccupied with fighting. It is also proven that when the Sahaabah besieged 
    Tastar, dawn came when the fighting was still going on and the people were 
    scaling the walls and were at the gates of the city, and they delayed Fajr 
    prayer until conquest was granted to them, then they prayed at the time of 
    duha (forenoon) so that they would not miss out on the opportunity to 
    conquer the city. In such situations it is permissible to delay the prayer. 
    If there is a fire in which Muslim people are trapped, it is permissible to 
    focus on rescuing them, even if that means that you will miss offering a 
    prayer on time, because saving Muslim lives which are protected by sharee’ah 
    is very important, and because it may not be possible to deal with this 
    danger except by delaying the prayer; the prayer is being missed for a valid 
    reason, so it is permissible to delay it. A person may also delay the prayer 
    and join prayers because of sickness and travelling, so it is permissible to 
    delay prayers until after their time or to delay ‘Asr or Fajr prayers from 
    their times in order to save one who is drowning or burning and so on. End 
    quote. 

    Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him)