In Night, by Elie Wiesel, how does Elie's loss of faith help his survival?

As a result of Eliezer's loss of faith, he places more importance on survival than on God.

It should be known that Eliezer does not claim that his survival takes place because he loses spiritual faith. Eliezer never claims that faith and survival are mutually exclusive.  However, he argues a nuanced point regarding religious identity.  Throughout Night, it is evident that when people possess faith in the divine, their entire lives are geared towards that end.  For example, Akiba Drumer sees no other purpose in his life outside of his spirituality.  Even though Akiba Drumer is in the midst of the death camps, he continues to believe in God and being saved.  While he walks towards the gas chamber, he continues to believe, asking those left behind to recite the Kaddish for his soul.  Akiba Drumer's life is an example of how religious faith means that God is the sole focus of existence.

Eliezer views reality in a different way.  His experiences lead him to believe that survival, not God, should represent his life's purpose.  Given what Eliezer experiences, he is unable to reconcile what he sees with a spiritual identity: "Master of the Universe, know that the children of Israel are suffering too much; they deserve redemption, they need it. But if, for reasons unknown to me, You are not willing, not yet, then redeem all the other nations, but do it soon!"  Eliezer's faith withers when he says that he "did not deny God's existence" but rather "doubted his absolute justice."  This is echoed in his idea that Hitler, not God, kept all his promises.  These revelations make it clear that survival, not God, was Eliezer's all-encompassing focus.  His loss of faith allows him to channel his thoughts towards survival and away from adhering to God and his laws. 

As a result of his loss of faith, Eliezer's mindset places a primacy on survival. He views himself as a creature who must endure.