Well the title of the Game IS Legend of Zelda, so it leaves space for link to die and pass on the triforce of courage to the next main character. It's possible but I for one won't want him to die.
umm like i just said, Link does die and he passes on the Triforce to another hero who just happens to be called Link.
also, incase no one ever noticed, the character is never really named Link in any of the games. you always input your name and thats the name that shows throughout the game. so unless you name your character "Link," he is never really even a character in the game.