It could be that they adopt a group of children. Some of them are demigods and some are mortals who were all in a difficult situation. Percy and Annabeth's home becomes a haven for these kids. They teach them all about Greek mythology, train the demigod kids in combat and powers, and for the mortal kids, they teach them how to support their demigod siblings. This would create a really unique family dynamic full of love, adventure and learning.
Their relationship would likely become more nurturing. They would have to rely on each other more as they take on the role of parents. For example, when the child has a nightmare about monsters, Percy might be the one to comfort the child first while Annabeth figures out how to better protect the home. Then they would discuss their concerns and fears for the child together, strengthening their bond as they face these new challenges as a couple.
One possible storyline could be their children going on a quest to discover a new hidden part of the demigod world. Maybe they have to find a lost artifact that is crucial for the safety of Camp Half - Blood. Another could be their children facing challenges at school, dealing with both normal school problems and the added pressure of being demigods.
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.
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.
It could be a child of a minor god who has been overlooked. Maybe the child of Hecate, a young demigod with some really interesting magic powers that Percy and Artemis see potential in.
Well, their son could inherit Percy's water - controlling abilities and Annabeth's wisdom. Maybe he'd be a hero in his own right, facing new threats in the world of the fanfiction. He could grow up trained by his parents and their friends, learning combat and strategy.
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.
One reason could be that she's scared. The idea of becoming a mother at that point in her life might be overwhelming, and she might think she can't handle it with Percy. Maybe she wants to protect Percy from the difficulties that come with the pregnancy as well.
One reason could be that Percy often gets into dangerous situations alone to protect others. Annabeth, being his friend or more, would feel bad seeing him constantly at risk.
In this kind of fanfiction, they might have an adventure together. Maybe they'll face a new monster that they haven't encountered before. For example, a mythical creature from a less - known part of Greek mythology.