There are two parts to the question. The first part is how well Elizer fares in the struggle to stay alive. The answer is that he does succeed in this quest. This is proven by the fact he is alive at the end of the narrative. The second part is naturally a bit more complex. The notion of "remaining human" is something whose definition changes over the course of the work. It might be difficult to suggest that he remains human by the end of the work because of the amount of changes he undergoes throughout the course of the work. For example, the typically human experiences of collectivity through community, connection with family, and faith in divinity are all repudiated throughout the course of the novel. It is not as if Eliezer chose to sever these bonds, but rather such choices were made for him, removing him from specific aspects of his humanity. In the end, when he stares at the mirror and is unable to recognize the face staring back at him, it is because his humanity has been robbed from him. I am slightly bothered by saying that he "failed" at his struggle to remain human because of this precise lack of autonomy.