Well, in some fanfictions, Sirius might abandon Fem Harry because he has some sort of secret mission that he believes is more important than staying with her. Maybe he discovers some dark prophecy related to Fem Harry and thinks that leaving her will change the course of events. Also, it could be that Sirius has his own inner demons, like guilt from his past, and he feels unworthy of being around Fem Harry so he leaves.
In some fanfictions, Annabeth could abandon Percy because of a prophecy. If the prophecy seems to imply that being with Percy will lead to a great disaster, she might choose to leave to protect him or the world. Also, it could be due to a personal growth arc for Annabeth. She may realize that she has been too dependent on Percy in the past and decides to go off on her own to find her true self, leaving Percy behind.
One possible reason could be ideological differences. Naruto firmly believes in protecting his village and his friends, while the Akatsuki has goals that often involve causing destruction and chaos. In fanfiction, Naruto might realize that the Akatsuki's actions go against his own values of peace and harmony, so he decides to abandon them.
One possible reason could be Sirius believing he can protect Harry better on his own. Maybe he thinks the Dursleys are too dangerous for Harry and that the wizarding world isn't doing enough. So, he decides to take matters into his own hands and kidnap Harry to keep him safe.
One possible reason could be that Harry is feeling extremely overwhelmed with the challenges he faces in the wizarding world. Sirius is like a father figure to him, so in front of Sirius, he can let out all the pent - up emotions. Maybe he's had a tough encounter with Voldemort or his Death Eaters, and the fear and stress finally break him when he's with Sirius.
Jealousy could also play a part. For example, if Harry starts getting closer to other mentors or friends, Sirius might feel left out and act out in a way that causes a fight. Or if Sirius seems to be spending more time on Order of Phoenix business than with Harry, Harry could feel neglected and start an argument.
A simple reason could be miscommunication. Maybe a letter from Harry got lost, or there was a misunderstanding in a conversation, and Sirius thought Harry didn't want to be around him anymore so he starts to ignore Harry in return.
One possible reason could be that he feels unsafe at Hogwarts. Maybe there are threats from dark wizards within the school that the teachers are unable to fully protect him from. Sirius, being his godfather, represents a safe haven.
One reason could be Harry's impulsiveness. Harry often jumps into dangerous situations without thinking, and Sirius, being his godfather and having a protective nature, would shout at him to make him realize the risks. For instance, if Harry decides to go after a Death Eater alone.
Maybe Dumbledore discovers some dark secret about Harry's past that he can't handle. It could also be that Dumbledore is trying to protect Harry in a really strange way, by pushing him away from the dangerous wizarding world around Hogwarts.
One reason could be disillusionment. Maybe he discovers that the wizarding world is not as noble as he once thought, with a lot of hidden political intrigue and corruption. For example, the Ministry of Magic might be misusing its power, and Harry, being a symbol of justice, can't stand it anymore.