One possible reason could be a change in character development that diverges from the original show's trajectory. Maybe in the fanfiction, the writer wants to explore new relationship dynamics where Castle has different feelings. Another reason might be to create conflict for the plot. By having Castle not love Beckett, it can lead to a series of events that test their partnership in a different way.
Maybe they stumble upon a government conspiracy. The government wants to keep something hidden and they are seen as a threat, so they are made to disappear. It could also be related to a scientific experiment gone wrong. They are in the wrong place at the wrong time and get caught in an energy field that transports them to an unknown location, causing them to disappear from their normal world.
The plot could develop as Beckett tries to figure out why Castle doesn't love her and in the process discovers something about herself. For example, she might realize she has been too focused on work and neglected her personal relationships.
Perhaps they are trying to protect their relationship from outside interference. For example, if there are people in Castle's publishing world or Beckett's police department who don't approve of their relationship, they could pretend to be separated to avoid any negative consequences. This would allow them to still be together in private while keeping up the appearance of being single in public. Also, it could be a way to test their relationship. They might want to see how they would fare on their own and if their feelings for each other are strong enough to withstand a period of 'separation'.
One possible reason could be that they are on a secret mission. Maybe they are trying to protect a key witness or important evidence from a powerful and dangerous criminal organization. In the world of fanfic, this could lead to them having to disappear to keep their whereabouts unknown.
Maybe he's afraid of losing her because she's his partner and they've been through so much together. Their relationship is very important to him.
It could also be a fanfic that takes place in an alternate universe. In this universe, the events of 4x23 didn't happen as they did in the show. Maybe Beckett didn't become a detective in the same way, and Castle meets her in a completely different situation. They then start to solve mysteries together in this new setting.
Maybe in the fanfiction, Vegeta has some personal growth that makes him focus more on himself rather than family. He might have new goals and ambitions that he thinks are more important than his relationship with Trunks.
One possible scenario could be a really emotional moment where Castle finally gathers the courage to express his deep feelings for Beckett through his fanfiction. Maybe he uses the stories he writes as a way to convey his love in a more creative and less intimidating way.
Some fanfictions center around their cases. They might expand on a case from the show that seemed really interesting but was not fully developed. For instance, a story could be written from the perspective of Castle and Beckett when they were on a particularly dangerous undercover mission. These types of stories add more depth and detail to the events that happened in the show.
One popular 'castle beckett fanfiction' story could be about their adventures in an alternate universe where they solve crimes in a steampunk - style city. Another might focus on their relationship development during a long - undercover mission.