Well, it could be that Asami discovers some big secret about Korra that she can't accept. For example, if Korra has been hiding a past relationship or some dangerous power she has. Asami might feel betrayed and break Korra's heart by ending their relationship.
Another possibility is that Asami's family or some external force pressures her to end things with Korra. Her family might have some old - fashioned views or some business - related reasons. They could convince Asami that being with Korra is not in her best interest. Asami, being torn between her family and Korra, finally decides to break Korra's heart by following her family's wishes.
Maybe Asami realizes she has feelings for someone else. This new person could have entered their lives and Asami finds herself drawn to them. In her confusion and new - found feelings, she decides to break things off with Korra, shattering Korra's heart in the process. She might tell Korra that she can't continue their relationship because she has found something different with this other person.
She could also get angry. Korra is a strong - willed character. After the shock wears off, she might lash out at Asami. She could yell and demand an explanation. She might feel that she has been wronged and wants Asami to know how much she has hurt her.
Perhaps in the fanfic, Asami has her own dreams and ambitions that Korra unknowingly hinders. For example, Asami wants to expand her company's business in a certain area, but Korra's actions as the Avatar cause political unrest in that region. Asami, feeling let down by Korra's lack of consideration for her goals, decides to break away from her. Another plotline could be that there's a misunderstanding. Maybe a false rumor spreads that Korra has feelings for someone else, and Asami, heartbroken, decides to end things with Korra.
I'm sorry, I'm not aware of specific 'Asami breaks Korra' fanfics. You can try searching on popular fanfic websites like Archive of Our Own or FanFiction.net.
One possible plot could be that Korra and Asami adopt a baby. They might find a baby who has special bending abilities and they decide to raise the child to help it control and understand its powers. They face challenges from the traditionalist elements in their world who are not accepting of their relationship or their decision to raise a child together.
In a Korra Gets Asami Pregnant Fanfiction, the plot might begin with Korra and Asami already in a loving and stable relationship. Asami discovers she's pregnant, which is a huge surprise. The story could then revolve around how Korra, being the strong - willed and protective partner, tries to ensure Asami has a smooth pregnancy. There could be elements of Korra using her bending abilities to help Asami in some way, like creating a comfortable environment for her. Also, the fanfiction could explore how their friends from the series react to the news, some being overjoyed and others maybe a bit worried. It could also touch on how they plan to raise the child in a world that is still recovering from the events of the original series.
One possible fanfic could be about Asami getting jealous when Korra spends a lot of time with another character. Maybe Korra has to work closely with someone on a new project in Republic City, and Asami starts to feel left out. Asami might try to hide her jealousy at first, but it eventually bubbles to the surface during a dinner with Korra and the others.
Perhaps Catherine constantly belittles Steve in public or in front of his friends. Over time, this emotional abuse causes Steve to feel unloved and unwanted, and his heart is broken. She might make him feel like he's not good enough for her, which ultimately leads to the breakdown of their relationship.
It could be that Hinata publicly humiliates Naruto. She might expose some of his deepest insecurities in front of the whole village. Since Naruto has always been striving for the village's acceptance, this betrayal from Hinata, who he loves, would be a huge blow to his heart.
Well, at first, they might be a bit nervous about how this new addition will affect their relationship. But as they care for the baby together, they would become more in sync. They would share responsibilities like Korra teaching the baby about bending and Asami teaching about technology. Their relationship would grow stronger as they face the sleepless nights, diaper changes, and first steps together. They would also become more protective of each other and the baby in the face of any threats or difficulties.
Love and friendship are very common themes. Most fanfics focus on how Korra and Asami's relationship grows from being friends to something more. They often show how they support and understand each other.