It could also be that Naruto is forced to leave Sakura due to some external threat or danger. For instance, if there is an enemy targeting Naruto and he fears that being around Sakura will put her in harm's way, he would choose to leave to keep her safe. This is in line with Naruto's selfless nature as seen throughout the series.
Maybe Naruto realizes that his feelings for Sakura are not as strong as he once thought. In the fanfiction, he could have met someone else or had an epiphany about his own emotions. He might leave Sakura to find his true self and explore different relationships.
In some fanfics, Naruto may ignore Sakura because he has his own emotional traumas to deal with. He might find Sakura's presence a reminder of things he wants to forget or move past, so he chooses to keep his distance. For example, if he has faced a lot of rejection from her in the past, he could decide to just cut her out of his life.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he wants to explore his own path independently and test his skills without Jiraiya's constant guidance.
One possible reason could be that Naruto has his own goals and missions that he is so focused on that he tries to avoid distractions, and Sakura might be seen as a distraction in some sense. For example, he is always aiming to become Hokage and improve his ninja skills, and any personal relationship drama could get in the way of that.
Another possibility is jealousy. Maybe in the fanfic, Sakura shows more interest in another character, like Sasuke perhaps, and Naruto, who has his own feelings for Sakura, snaps out of envy. It's a common trope in fan - made stories to play with the characters' emotions like this.
Another reason could be a very dark and alternative interpretation of the characters. Maybe the writer has a different view of Naruto's character arc and how he could be pushed to the extreme. And they see Sakura as a character that could be sacrificed in this extreme version of Naruto's story. But this is a very far - fetched view considering the original story's development.
One reason could be that she realizes she has been too dismissive of Naruto's feelings for her. She might have led him on or been cruel in rejecting his advances in the past. Another reason is that she finally understands how much Naruto has sacrificed for the village and for her personally, and she feels guilty for not showing him more respect and gratitude earlier.
One possible reason could be to seek stronger opponents outside of Konoha. Naruto might feel that he has outgrown the training opportunities in the village and wants to face greater challenges.
One reason could be that Naruto realizes his feelings for someone else and doesn't want to mislead Sakura. In some fanfictions, Naruto might discover that his true love is Hinata and so he steps away from Sakura to pursue a relationship with Hinata without causing any confusion for Sakura.
One possibility is that Naruto realizes Sakura has feelings for Sasuke that he can't change, so he decides to focus on his own ninja journey alone and leaves her to figure out her relationship with Sasuke. He might feel that his presence is only causing confusion or getting in the way of her true feelings.