This a great question. Amir is a complex character and there are a few reasons why his mother's death is painful to him. A bit of context is important here.
First, Amir's did not know his mother. She died giving birth to him. Second, his father Baba had an affair with another women and she bore him a son, Hasan, who is the household servant's son. Both of these point will be important in understanding Amir and his relationship with his father.
Amir feels responsible for his mother's death. This is, of course, irrational, as it was not his fault, but he cannot help but feel guilty.
What is worse than this feeling perhaps is he feels that his father, Baba also holds him responsible for his mother's death. This not only adds to the guilt, but also creates distance between him and his father. As you can imagine, the situation is far more complicated, because part of the distance between Baba and Amir is due to Hasan. The lives are complicated, but in truth Baba loves Amir.
Aside from the fact that Amir never saw his mother and that he feels the guilt of causing her death during childbirth--and believes that Baba blames him as well--Amir knows very little about his mother. Although his relationship with Baba may seem distant, he has spent his entire life absorbing the ways of his father, and the two have grown much closer during their stay in California. But
Baba had always described my mother in broad strokes, like "She was a great woman..." (Chapter Twenty)
and Amir knows little about Sofia Akrami, who had been a teacher at the university in Kabul. Her only legacy to her son is "my dead mother's books." Amir must realize that he was much more like his mother, well-read and well-educated with a love for books, and that his own life would have been much different with her love and influence. When Amir meets the ragged beggar, Dr. Rasul, on the streets of Kabul, he discovers the old man knew his mother, and he begs for just a few bits of information about her. Whatever he may remember is more than Baba shared--"Baba took his memories of her to the grave with him." Amir comes away with the knowledge that she
... liked almond cake with honey and hot tea, that she'd once used the word "profoundly," that she'd fretted about her happiness. I had just learned more about my mother from this old man on the street than I ever did from Baba. (Chapter Twenty)
With Baba dead, Amir is able to piece together a few new facts about his mother as he tries to shape his own new identity--one different from simply being the son of the great man, Baba.