The comic often tells tales of Dr. Rex Morgan dealing with various patients, their illnesses, and the challenges that come with providing medical care. It also explores his interactions with colleagues and his own life outside the hospital.
In the Invincible comics, Rex survives. The character's fate takes different turns, but death isn't one of them. The storyline keeps him involved and active throughout.
Rex Splode remains alive throughout the comics. The storylines don't feature his death. Maybe there were some close calls or dangerous situations, but he survived them all.