In the fanfic, it might be that Naruto has new responsibilities in the village that are more important than chasing Sasuke. For example, he could be needed to deal with new threats to Konoha, so he has to let go of his personal mission to bring Sasuke back.
Well, it could start with Naruto having an internal struggle. He might have a moment of realization that chasing Sasuke has cost him a lot and isn't really getting him anywhere. So he decides to focus on other things, like training new ninja in the village.
One possible reason could be that the author wants to focus on other characters. Maybe they feel that Naruto's story has been told enough in the fanfic and it's time to give other characters the spotlight.
In the fanfiction, Naruto could stop chasing Sasuke because he has a moment of self - realization. He might understand that his own identity and purpose in life are not solely defined by bringing Sasuke back. He could find new goals and dreams that don't involve Sasuke. Also, there could be a major event in the ninja world that makes Naruto shift his focus away from Sasuke, like a new and powerful enemy that threatens the entire village or region.
It could be that Naruto has outgrown his initial feelings. As he matures, he starts to view Sakura more as a friend. In the fanfic, his experiences in the ninja world might have changed his perspective on love. He might have seen so much pain and sacrifice that he no longer wants to hold on to a love that might be one - sided or not as fulfilling as he once thought. Also, Sakura's continued love for Sasuke in the fanfic could be a factor that makes Naruto step back.
One reason could be Sasuke's continued pursuit of revenge. If in the fanfiction, Sasuke is so consumed by his need for revenge that he neglects Sakura and their relationship, it might cause her to stop loving him. Another reason could be that Sakura discovers a side of Sasuke she doesn't like, like a cruel streak.
Another reason could be that Hinata herself undergoes a significant transformation. Maybe she has a spiritual awakening or a change in her life goals that make her realize that her love for Naruto was more of an infatuation based on her younger self's ideals, and as she grows, she no longer feels the same way.
One possible reason could be that Naruto realizes Sakura's unrequited love for Sasuke. He might feel tired of always being in a one - sided emotional situation with her. Another reason could be that Naruto has his own goals and growth to focus on. His journey to become Hokage and protect the village requires all his attention, leaving little room for his previous feelings for Sakura.
One possible reason could be that Naruto has faced too many betrayals. Maybe his friends turned on him in the fanfic, which made him lose faith and stop caring.
One possible reason could be that the fanfiction author wants to focus on other characters. Maybe they feel they've explored Naruto's character enough and want to give more spotlight to characters like Sasuke or Sakura. Another reason might be that the plot of the fanfiction takes a turn where Naruto's acting skills are no longer relevant or needed.
One possible reason could be that it goes against the original dynamic between Naruto and Sasuke. In the original story, their relationship is based on a deep male - male bond of rivalry and friendship. Changing Sasuke to a female might disrupt that established connection.