Another possible reason could be political intrigue within the wizarding world. There could be a faction that wants to isolate Harry, and they manipulate the Gryffindor house into banishing him. They spread false rumors about Harry being a threat to the safety of the other Gryffindor students, which causes panic and eventually leads to his banishment.
In some fanfictions, it could be due to a misunderstanding. Maybe someone framed Harry for a serious rule violation that Gryffindor's house values highly, like cheating in an important magical exam. And the evidence against him seems so strong that the Gryffindor house decides to banish him.
In some fanfictions, it could be a political move within Hogwarts. There might be a group that wants to undermine Dumbledore's influence, and since Harry is so closely associated with him, they target Harry by getting him banished from Gryffindor. This could also be related to the discovery of some long - hidden secret about Harry's family that makes the Gryffindors view him differently.
Another reason could be related to a new prophecy. Suppose a new prophecy emerged that said Harry Potter's presence in Gryffindor would bring great danger to the house. The Gryffindor students and faculty, believing in the importance of protecting the whole house, might have decided to banish him. But of course, this would be a very difficult decision as Harry has been an important part of Gryffindor before. And in the end, the prophecy might turn out to be misinterpreted.
Maybe he was too busy dealing with the real threats in his life, like Voldemort and his Death Eaters. Fanfiction might seem unimportant compared to the real battles he had to face.
One reason could be a falling - out with his friends in Gryffindor. Maybe there was a misunderstanding that grew so large that he felt he couldn't stay. Another possibility is that he might be lured away by some mysterious force or character who convinces him that Gryffindor is no longer the right place for him. For example, if a new group claims to have a better way to fight Voldemort and they are from a different 'house' in this fanfiction concept.
In some fanfictions, Harry could become withdrawn and depressed at first. Losing his place in Gryffindor is like losing his family. But then, he might find new strength and purpose, perhaps by joining forces with some outcasts in the wizarding world and forming a new group that challenges the unjust actions of Gryffindor house.
One possible reason could be a fallout with his friends in Gryffindor. Maybe he feels betrayed by them in some way in the fanfiction world. For example, if they wrongly suspect him of something.
One reason could be that he doesn't like the spotlight that comes with being a Gryffindor. In the original story, Gryffindors are often in the limelight, and in fanfiction, he might be tired of all the attention.
One possible reason could be a major disagreement with the Gryffindor house leadership or some of the students. Maybe he feels that they are not living up to the values he thought they held. Another reason might be that he discovers some dark secret within Gryffindor that makes him uncomfortable and he decides to leave.
Perhaps he leaves Gryffindor in fanfiction because he is influenced by a new mentor or friend who is from a different house or group. This person might convince him that he can achieve more or be more true to himself outside of Gryffindor. Also, it could be due to a prophecy or a special mission that requires him to distance himself from Gryffindor for a while to protect the house or the entire Hogwarts from a certain threat.
He'd probably be devastated at first. Gryffindor has been his home at Hogwarts, and his friends are there. But he's also a resilient character. He might start to question the fairness of the banishment and try to prove his innocence. He could look for allies outside of Gryffindor, like Luna from Ravenclaw, who might believe in him.