One reason could be that the writer has outgrown the Naruto fandom. As people grow and change, their interests shift. They might find other anime or stories more appealing now.
One possible reason could be to search for a new power source. Maybe in the fanfic, the powers within the Elemental Nations have become stagnant for him, and he believes there are greater sources of power elsewhere.
In some fanfics, Naruto might leave Konoha as a child because he feels ostracized. Since he's the jinchuriki of the Nine - Tails, many villagers fear and shun him. He could get tired of the constant cold shoulders and decide to leave in search of a place where he'll be accepted.
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 for his safety. Konoha is a well - protected village with many skilled ninja. She might believe that leaving him there would ensure he has the best chance at survival and growth as a ninja. Also, she may have some mission or obligation that forces her to leave him behind, perhaps something related to the greater good of the village or the ninja world in general.
One possible reason could be a conflict within the team. Maybe Naruto felt misunderstood by Sasuke or Sakura. Another reason might be a mission gone wrong where Naruto blames himself and decides he's a liability to the team. Or perhaps he gets an offer from another group that he believes can help him achieve his goals faster.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
One reason could be to seek more power. In some fanfictions, Naruto might feel that the Leaf doesn't offer enough resources or training for him to reach his full potential. So he decides to leave to find a place where he can grow stronger.
One possible reason could be a difference in their goals. Naruto is from the Hidden Leaf Village with a mission to protect it and promote peace there. Rias, on the other hand, has her own responsibilities in the Underworld. Their conflicting duties might lead to Naruto leaving.
One reason could be that Naruto might feel he has outgrown Jiraiya's teachings in the fanfiction. He may want to explore his own path independently. Another possibility is that Naruto gets involved in a mission or a situation where he has to part ways with Jiraiya for the greater good. For example, if there is a threat in a far - off land that only Naruto can handle, and Jiraiya has other commitments elsewhere.
One reason could be to gain more power. In many fanfictions, Naruto realizes that the threats he faces are far greater than what he can handle with his current skills in Konoha. So, he decides to leave and train in a more secluded and challenging place to enhance his abilities.