Should I continue waking my brother for prayer despite his lack of response and delay in performing it, or should I let him sleep?

Scholars differ on the obligation of waking a sleeping person for prayer. If waking your brother would make him defiant and cause him to delay the prayer further, taking it outside its prescribed time, then it is not permissible for you to wake him. The sin falls away from you, and the sin is upon him for his heedlessness and negligence regarding his prayer. It is incumbent upon a Muslim to maintain prayer at its legally prescribed time. Allah the Almighty says: "Guard strictly the prayers, especially the middle prayer; and stand up before Allah with devotion." [Al-Baqarah:238], and Allah the Almighty says: "Indeed, prayer has been decreed upon the believers a book at specified times." [An-Nisa:103]. Allah has warned those who delay prayer beyond its time without a valid excuse, saying: "So woe to those who pray [But] who are heedless of their prayer" [Al-Ma'un:4-5].