In some fanfictions, it could be due to a misunderstanding. For example, Percy might be involved in a quest where things seem a bit shady, and Annabeth misinterprets his actions as something more malicious. Also, the stress of their demigod lives could take a toll on their relationship. Constantly facing monsters and life - threatening situations can make them short - tempered with each other, and over time, it could lead to a break - up.
One possible reason could be differences in their long - term goals. Maybe Annabeth is more focused on her architectural dreams and wants to study in a far - off place, while Percy is more tied to the demigod world in Camp Half - Blood. Another reason might be jealousy. If Percy spends too much time with other demigods, especially female ones, Annabeth could feel left out and insecure, leading to the break - up.
Perhaps a prophecy comes into play. A prophecy that requires Percy to be alone or with someone else for the greater good of the demigod world. Annabeth, being the logical and selfless person she is, might decide to break up with Percy to ensure the prophecy is fulfilled and to protect the demigod community as a whole.