................... the timely medical attention the patient would have died

A: "In spite of" this phrase doesn't fit the context because it doesn't convey the idea that medical attention prevented the patient's death.

B: "Because of" this doesn't fit because it suggests the patient would have died because of the medical attention, which is not the intended meaning.

C: "But for." This phrase means "if it weren't for" or "without the presence of." It's used to indicate that something prevented another event from happening. In this context, "But for the timely medical attention, the patient would have died" means that if the medical attention hadn't been provided, the patient would have died. This fits perfectly with the intended meaning. 

D: "Even after." This phrase implies that something happened despite a preceding event. However, this doesn't convey the idea that the patient's life was saved because of timely medical attention, but rather the opposite.

Therefore, Option C is the correct answer.