Another possible reason is that Naruto's goals and dreams as a ninja become so all - encompassing that he simply doesn't have time for Sakura. His pursuit of power, knowledge, or the protection of the village takes precedence. He may see Sakura as a distraction from these more important matters and thus starts to ignore her.
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.