Another reason could be that Naruto is trying to protect Sakura in his own way. He might think that by ignoring her, he can keep her out of harm's way. If he senses that there are dangerous enemies lurking around, he could be trying to create a distance between them so that Sakura doesn't get caught up in any potential battles or threats.
One possible reason could be that something happened during the Kage Summit that made Naruto lose trust in Sakura. Maybe she made a decision or took an action that he didn't agree with. For example, if she sided with someone against Naruto's ideas regarding the situation at the Summit.
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.
Sakura might initially be confused. She would probably wonder why Naruto is acting this way all of a sudden. For example, she might try to get his attention by calling his name a few times, but when he doesn't respond, she could be left feeling a bit bewildered.
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.
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 that Naruto sees something in Sai that others don't. Maybe Sai has a unique way of understanding Naruto's pain or his dreams. Another reason might be that Sai represents a new beginning for Naruto. Since Sai has a different background compared to the others, Naruto might find his perspective refreshing and be more drawn to him.
One possible reason could be that Sakura has finally grown tired of Sasuke's aloof and cold behavior towards her. She might have realized that she has been constantly chasing after him while getting little in return, so she decides to ignore him as a form of self - preservation.
One possible reason could be that Naruto has grown tired of Sakura's violent tendencies towards him. He might have reached a point where he decides to stand up for himself and not tolerate being hit any longer.
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.
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.