Perhaps she made a mistake during a mission that she thought put everyone in danger. Annabeth is a perfectionist, and any error on her part would be hard for her to bear. Percy would comfort her by reminding her of all the times she's saved them, and that everyone makes mistakes. He'd probably give her a warm hug and tell her they'll get through it together.
It could be that she's homesick. Despite all the adventures, sometimes the longing for home can be overwhelming. Percy would comfort her by sharing his own feelings of missing his mother and how they can make new homes with their friends. He might hold her hand and tell her that their friends are like family now.
He gives her a big hug. Physical contact can be very comforting, and Percy's hugs are always warm and reassuring.
It could be that he's lost someone important. Percy has had many friends and family in his life, and if he loses one of them, it would be a huge blow.
Well, perhaps it could be about a great battle where Percy sacrifices himself to save his friends or the world. Annabeth then cries because she has lost her beloved Percy. Maybe she blames herself for not being able to protect him, and the rest of the story could be about how she copes with this great loss, like she might try to carry on Percy's legacy or find a way to bring him back in some magical way.
Perhaps it's part of their banter. In their relationship, they often tease each other. Annabeth calling Percy stupid could be a form of affectionate ribbing, not actually meaning that she thinks he's truly stupid but just a way to playfully get on his nerves.
One possible reason could be miscommunication. Maybe Annabeth made a decision without consulting Percy in the fanfiction, and Percy felt left out or betrayed, leading to his screams.
Perhaps Percy refuses to take on a certain task that Annabeth believes is crucial. It could be something related to saving a friend or retrieving an important item. His refusal might seem cowardly to Annabeth, without her realizing that Percy has some other valid concerns or reasons for not doing it right away.
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.
The popularity also comes from the fact that both characters are very well - loved. Percy is brave and kind, and Annabeth is intelligent and strong. Seeing Percy be there for Annabeth gives fans a sense of warmth. For example, in the original books, they've been through so much together, and fanfiction allows fans to explore more of those tender moments of comfort. It gives a chance to delve deeper into their relationship, beyond what was shown in the main series.
One great Percy Comforts Annabeth fanfiction could be 'A Shoulder to Lean On'. In this story, Percy finds Annabeth after she has a nightmare about Tartarus. He holds her close and tells her that they are safe now, and he won't let anything bad happen to her again. His kind words and warm embrace slowly ease her fears.
Yes, there are quite a few. You can start by looking on fanfic websites like Archive of Our Own. Some fanfics might focus on Percy being there for Annabeth during her tough times in Camp Half - Blood, like when she's stressed about a quest or having problems with other campers.