The original question had to be edited down. I think that one of the challenges that Erica and Changez face is cultural. The period after the September 11 attacks proves to be a period in which their cultural differences could not be fully navigated. Both are unable to understand the cultural reality of the other in a time period during which culture defined so much about one's reality. The discrimination and prejudice that litters the post- 9.11 landscape ends up impacting both of them, revealing a challenge that neither could fully navigate. Cultural differences proved to be a challenging element. The book displays their relationship disintegrating as a result of this.
I would suggest that there is another challenge that proves to be even more arduous for them. Neither one is shown to fully understand the sacrifice of self that is needed for a relationship to work. Neither one of them can relinquish their own sense of self. This becomes a challenge that can be seen as superseding culture. Changez initially looks at his relationship with Erica as part of his fulfillment of "the American Dream." Changez's love with "America" and "Erica" are one in the same. He is in love with the idea of both. He is incapable of seeing the other in a realistic and full manner, complex and filled with flaws. Instead, he embraces both as a part of an illusion, making its sustainability impossible. Erica is much the same. She is unable to see the present and embrace it outside of her own understanding of the past. Her inability to let go of her own past in making something work in the present is a challenging element in their relationship that is impossible to overcome. Erica is unable to surrender what was in the past in light of the present. For Erica, this inability is what dooms any chance of this relationship working. While culture is shown to be a challenging element for both, the reality is that there is an emotional construction of self that makes sustaining this relationship a challenge that cannot be overcome.