Draco could have developed a new - found respect for Harry. After seeing Harry's courage and determination over the years, he might come to admire him. This admiration could turn into a desire to protect Harry from Voldemort, especially when he realizes that Voldemort's actions are only leading to more death and destruction.
One motivation could be self - preservation. Draco might realize that if Voldemort kills Harry, it will lead to an all - out war that could destroy everything he knows. By saving Harry, he hopes to find a more peaceful solution and protect his own family and the wizarding world in a broader sense.
Perhaps he realizes that Harry has potential that can be used for his own purposes rather than just killing him. So he wants to keep Harry close and away from the Dursleys who are just muggles.
Maybe Draco discovers a hidden weakness of Voldemort. Draco, having been raised in a pure - blood family, might have access to some ancient magic knowledge. He uses this knowledge to create a situation where Voldemort is temporarily incapacitated, giving Harry the chance to escape or defeat Voldemort. For example, he could find a way to disrupt Voldemort's connection to his Horcruxes for a short time.
Love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him. He couldn't save Lily, but he can try to keep her son safe.
Love. In fanfictions, it's a common motivation. Draco might have fallen in love with Hermione over time, and that love drives him to risk his life to save her from Voldemort.
It could be that Draco is following orders from some dark forces. They see Ginny as a way to get to Harry, and Draco, being their follower, tries to target Ginny. He might think that by getting Ginny, he can gain more power or favor within those dark circles.
Sirius might see Draco as just a young boy being influenced by a bad father. He could have a sense of wanting to protect the innocent, regardless of which side they seem to be on. So he steps in to save Draco from Lucius' potentially harmful actions.
Well, Harry might save Daphne from Draco because Harry is always the hero type. He doesn't like Draco's pure - blood supremacist attitude. Daphne could be a target of Draco's cruel remarks or actions just because she might not fully conform to Draco's ideas. Harry, being the defender of the underdog in many cases, steps in. Also, it could be that the plot of the fanfiction is building a new alliance or relationship web, and Harry saving Daphne is a key part of that, leading to new story developments.
One motivation could be Snape's sense of duty as a teacher. Despite his dislike for Harry in some ways, he still has an obligation to protect the students. So, when he sees Lockhart endangering Harry, he steps in.
Draco might be motivated by jealousy. He could be jealous of Ron and Hermione's friendship or a possible romantic relationship between them. So he tries to harm Hermione out of spite.
It could be that Snape wants to spite Vernon. Vernon represents everything that Snape despises about Muggles who are cruel and unaccepting. By saving Harry from Vernon, Snape is showing his superiority over Vernon and also his power as a wizard. And of course, there's still that underlying reason of his love for Lily which makes him want to protect her son.