What might account for the fact that Eliezer and his father were able to keep their sanity while others slipped into madness?

I think their love for each other is foremost. They stay alive to help each other. The Nazis systematically tried to destroy family bonds. Elie and his father held on to these bonds both as a testament of love and an act of rebellion. Also their devout sense of God helped but Elie did feel his faith changing and even slipping away. Elie was also able to emotionally turn himself off and simply exist in the moment.