Maybe Percy is facing challenges that he can't easily overcome. For example, if he's in a magical world, he might be surrounded by more powerful characters. It could also be that he has made some mistakes and is overly critical of himself. Or perhaps he's being compared unfavorably to others in the fanfic world.
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.
One possible reason could be that she constantly compares herself to others in the fanfic. Maybe she sees other characters achieving great things or having qualities she believes she lacks.
One possible reason could be a misunderstanding. Maybe Annabeth made a decision without consulting Percy, like choosing a quest that she knew was dangerous but didn't tell him until it was too late. Percy might feel left out and mad about it.
One possible reason could be Percy's recklessness. He often jumps into dangerous situations without fully thinking them through, and Annabeth, being the more strategic one, might get frustrated and yell at him for endangering himself and others.
One reason could be that he values his mortal connections. His relationships with his friends and family are deeply rooted in the mortal world. Immortality might separate him from them, as they would age and die while he remains unchanged. For example, his bond with his mother is very strong, and he wouldn't want to lose that human connection.
One reason could be his heroic nature. Percy has accomplished many great deeds, and Aphrodite might be attracted to his courage and selflessness. Another could be his unique connection to the water, as Aphrodite has an appreciation for beauty and Percy's control over water could be seen as a beautiful and powerful thing in her eyes.
Another reason might be that she is forced to leave. There could be a magical or divine force at play. Maybe a god or goddess, who has some grudge against Percy or his father Poseidon, manipulates the situation so that Sally has no choice but to abandon Percy. This would add a lot of drama and conflict to the fanfic.
In fanfiction, Naruto could feel sick due to overusing his chakra. He often pushes himself to the limit in battles and training, and this excessive chakra use might take a toll on his body, making him feel ill.
It could be due to some sort of poison or magical spell. In the Percy Jackson universe, there are all kinds of creatures and magic that could cause such a reaction. For example, if he was exposed to a slow - acting venom from a mythical beast, it might gradually make him faint.
Perhaps he's feeling guilty about something that happened during one of his quests. Maybe he made a decision that had negative consequences for someone he cares about, and that's weighing on him. It could also be that he's just had a really tough encounter with a powerful enemy and is letting out the pent - up stress and fear through crying.