Is it permissible to delay a prayer—such as the Asr prayer—past its prescribed time due to necessity if the surgeon, during a surgical operation, fears for the patient's life if he were to leave his place?

The physician must observe prayer times. If necessary, it is permissible to combine prayers by performing them earlier or later (such as Dhuhr with Asr, and Maghrib with Isha). As for prayers that cannot be combined (such as Asr and Fajr), if it is possible to perform them in their time by alternating shifts, that is better. If not, there is no harm in delaying the prayer and making it up after the operation concludes due to necessity.