Previous posters have referred to Elie's faith for his reason for survival. If they mean faith in God, I'd have to disagree because he abandons God quite early in his concentration camp experience. Elie does seem to have a tremendous amount of faith in himself, especially as time goes on. He is able to get more "street smart" by finding ways of getting out of dangerous situations. His youth is also a good answer, as mentioned above. Though he began weaker than some of the adults, he physically matured as time went on and was better equipped to handle the death marches and other feats of physicality. Elie watched as some of the stronger men dropped dead, but he managed to endure through it. Also, though it was never mentioned, I wonder how much he thought about staying alive in hopes of being reunited with his mother and sisters.
I would say that one of the factors that helps Eliezer survive lies in his ability to understand the reality of situations. Others that fail to grasp the conditions around them are ones who perish. For example, when Eliezer is told to lie to say that he is 18, there is a choice he has and it's not luck that he decides to follow the advice of others. Another example would be on the train to Buchenwald, where Eliezer sees a father beaten to death by his son for the extra ration of bread, Eliezer grasps the condition and the severity of the situation in that the state of affairs has devolved to a particular level where individuals are killing one another for bread. Eliezer recognizes this and simply seeks to be anonymous in such a setting. I think that Eliezer's condition as someone who is able to recognize the demands of a particular situation and act in a manner that represents an appropriate response to that situation is what enables him to survive and endure. It should be noted that I am not certain that the tone of the work should be seen as a survival narrative. Rather, it is one in which Eliezer is "condemned to live as long as God himself," as he says upon seeing Auschwitz. The need to survive seems to be driven by a need to remember and serve as recorder to God's deeds during the Holocaust.
Elie's attitude was important. He also had people protecting him. He was intelligent, and he know how to move without being noticed. He was able to survive because he was mentally and physically healthy. Strong health in the first place would have been very important to survival.
Elie would not have survived without his faith. He begins as a young boy of extraordinary faith, and it is this which carries him through his ordeal for a long time. It's true that he doubts, that he gets angry at God, and even that at one point he renounces his faith; however, it is so much a part of who he is that it is a sustaining force for Elie long enough to help him survive.
A second factor is that he is not alone. At the beginning of their ordeal, Elie's father cares for him and protects him as much as can be done in this environment. Near the end of their journey together, the roles are reversed. It is true that Elie considers, at times, giving up on his father; however, he does not. It is his faith, it seems to me, which keeps him from doing what others around him do--give up or let their fathers die.
Another thing which helps him survive is his youth. He survives each selection by proving that he is strong enough to continue working. He survives the death run to Gliewitz simply by being physically able to endure it, even with an injured foot. Certainly there is something to be said, too, of "mind over matter" which Eliezer clearly displays throughout his imprisonment, but he must have also been physically strong.