Algernon did die in the story. Probably because he became too smart and his mind soon after deteriorated that he couldn't take it anymore. If I remember correctly, he starved himself to death. Burt's...
He doesn't die 'in the story' but he is going to have a bad situation. He brain is to deteriorate to the point lower than that he started out at, he may no longer be "highly functional". The story...