The question of Eliezer's sense of duty to his father is portrayed obviously with some bias, since Night is told solely from Elie's own perspective. Therefore, although Elie describes himself as supporting his father in almost every difficult situation they face, he does also include a few scenarios in which he obviously sees himself of falling short. Whether the reader agrees with Elie's assessments of his failures is a more complex and more personal question to answer.
Elie chronicles several times when he saved his father's life and/or supported his father during difficult periods. In chapter 4, when Elie's father is continually getting in trouble with Franek for his inability to march in step, Elie coaches him, despite the mockery he receives from his fellow inmates. In chapter 6, as the men, including Elie and his father, are being moved to Gleiwitz, Elie begins to feel extremely weak and considers dying. However, he says, "I had no right to let myself die. What would he do without me? I was his sole support." So, for his father, Elie keeps running.
At the very end of chapter 6, the SS do a selection in which Elie's father is identified as too weak and therefore would be killed. Elie saves his father's life by running to the other side and causing confusion among the groups. Though others are killed in the confusion, Elie is able to successfully sneak his father back to the other side to continue. Once they arrive at Buchenwald, Elie's father becomes more and more ill. However, Elie does not give up hope in trying to save his father's life. He continues to share his ration and asks multiple doctors for help.
Elie's own relationship with his father is juxtaposed several times with other examples of father-son relationships in the memoir. Elie recounts, in chapter 6, the rabbi's son intentionally leaving his father behind during the death march because he assumed his father was too weak to make it. Elie pleads that he never do what that son did. Then, in chapter 7, Elie tells the horrifying story of the son killing his own father for bread that is thrown into the train car that the father got for himself and his son to share.
All of these accounts are coupled with Elie's own obvious guilt over the moments where he did not perhaps do as much as he thought he should for his father. The majority of these moments occur in chapter 8, which is the chapter in which Elie's father is ill and dies. One of these instances is when he is given advice to take his father's ration for himself. Elie recounts,
He was right, I thought deep down, not daring to admit it to myself. Too late to save your old father ... You could have two rations of bread, two rations of soup. It was only a fraction of a second, but it left me feeling guilty.
Later in the chapter, Elie's father is struck by the SS officer when his father calls his name. Elie says,
I didn't move. I was afraid, my body was afraid of another blow ... I could see that he was still breathing—in gasps. I didn't move.
Elie's choice to remain still is what perhaps haunted him most of all. That night, his father is moved to the crematorium. "His last word had been my name. He had called out to me and I had not answered."
Despite these two instances, Elie does indeed remain faithful and dutiful to his father overall. The moments of his inaction can be clearly tied back to Elie's own fear and personal struggle for survival amidst horrific conditions. His acts of kindness, sacrifice, and love for his father are evident throughout the entire story and are what should be highlighted.