What is the major conflict in The Notebook?

The major conflict of the story has its roots in the past.  The "notebook" is an accounting of the life of Allie and Noah.

Allie and Noah are from the same town, but different sides of the tracks.  As Allie "grows up," she grows away from her small town associations and seems on track to a life of a sophisticated wife, married to a man of wealth and potential--she is engaged to marry another man (Lon), but pays one last visit to Noah.  It is at this point that their relationship is rekindled and Allie leaves Lon for Noah.

The conflict arises many years after Noah and Allie marry. They have a good life, children and grandchildren, but Allie gets Alzheimer's disease, and cannot recall the past.  She remember little bits and pieces from time to time, but then retreats to a place where she no longer recognizes her family--even Noah, the love of her life.

Noah patiently reads to the aging Allie from his notebook each day.  As each day begins, she believes that her "friend" Noah is telling her someone else's story.  It is "their" story, but most often she does not remember.  Though it breaks his heart to feel as if he is losing more of Allie each day, Noah continues to tell their story, and he finds great joy when she sees in him the man she married so many years ago.