One possible reason could be that she might be facing some sort of internal conflict. Maybe she has some unresolved issues from her past that resurface and make her feel like she can't be a part of Percy and their daughter's life. It could also be that she feels pressured by some external force, like a new threat in the world of the fanfiction that she believes she has to face alone and in doing so, she has to leave them behind.
Percy is likely to be heartbroken. He may initially be in a state of shock, not being able to believe that Annabeth has left him and their daughter. He might feel angry as well, feeling betrayed by her sudden departure.
It could also be due to some sort of magic or mind - control. A powerful enemy might have cast a spell on Annabeth, forcing her to turn against Percy. In this case, it's not really her own will but the result of external manipulation.
Well, one possible reason could be that Percy made a really stupid decision without consulting Annabeth first. Like, if he went off on a dangerous mission on his own when they were supposed to be a team. Annabeth is a very strategic person and she might feel betrayed or extremely frustrated by such actions.
In some fanfictions, Naruto might abandon his family due to a false prophecy that convinces him he's a danger to them. He may think that by leaving, he can protect them from harm that might come his way because of his past or enemies.
Maybe he was hit by some magic or a spell that affected his memory. It could also be due to some sort of trauma he experienced that made his mind block out his memories of Annabeth.
Perhaps Annabeth made a decision without consulting Percy that put him in danger. In the fanfiction world, this could lead to her feeling guilty and apologizing. For example, if she led their group into a trap because of her over - confidence, she'd realize her mistake and say sorry to Percy.
One possible reason could be a misunderstanding. Maybe she saw Percy doing something that she misinterpreted as a betrayal of their friendship or their cause. For example, if Percy was seen talking secretly with an enemy, Annabeth might jump to conclusions without knowing the full story.
Maybe she's scared because the fanfiction portrays Percy in a way that's out of character for him. Like, it might show him being overly aggressive or having strange powers that she doesn't recognize, which makes her feel like she doesn't really know him anymore.
It could be due to a misunderstanding. For example, Percy might have done something that Annabeth misinterpreted as betrayal or insensitivity. This could have led to her feelings changing or fading away in the fanfiction.
One possible storyline could be that their daughter inherits both of their special abilities. For example, she might have Percy's skill with water and Annabeth's strategic mind. She could go on adventures in the same world as her parents, facing new monsters and challenges. Maybe she discovers a long - lost secret related to the gods that her parents were unaware of.