A doctor can take leave if it is necessary. If the patient is in a hospital, he would be taken care of by another doctor in the hospital. There is no negligence on the part of the doctor in such a case. 

"A Doctor, like any other professional can take leave if felt necessary by him on account of his personal reasons or otherwise. If that happens it is for the hospital in which the patient is admitted to make alternative arrangement for the treatment of the patient in the hospital… the patient was admitted in a hospital and not in the clinic of Dr X, who could not have been expected to remain with the patient or in the hospital 24 hours of the day. Like other normal human being he also needs to take rest and his meals and then get ready for the duty to be performed on the next day. Therefore, there was no negligence on the part of Dr. X in leaving the hospital and the patient being treated by Dr Y in his absence." [Shri Manishbhai Kantilal Joshi vs Sheth P. T. Surat General Hospital, Surat, National Consumer Disputes Redressal Commission, New Delhi, Consumer Case No. 366 of 2014, dated: 09 Feb 2016]