One reason could be stress. Maybe they are in a really tough situation in the fanfiction, like facing a powerful enemy. Annabeth, being under a lot of pressure, snaps at Percy if she thinks he's not taking things seriously enough. Another possibility is jealousy. If Percy gets a lot of attention from someone else, Annabeth might snap out of insecurity.
It could be that Annabeth has her own personal issues or fears that she's dealing with. She might be worried about her future, her family, or her own abilities. And Percy, perhaps unknowingly, does or says something that triggers her. For instance, if he accidentally reminds her of a past failure or a fear, she could lash out at him.
In some fanfictions, miscommunication plays a big role. Percy might say something that Annabeth misinterprets. For example, he could make a joke about their relationship or their quest that she takes the wrong way. Also, if Percy makes a decision without consulting Annabeth first, especially if it's a risky one, she could snap at him. She values being part of the decision - making process.