I think it's because everything seemed to have been in vain. Like, her friends had "broken", she had no power against the devil. They never stopped to think what would happen if the time he gave the original FL ran out, and when it did, he made her think that she couldn't do anything else. After all, she managed to leave school, and this is what she found. Seeing her friends screaming, miserable, with a demon in front of her who has all the power against them and nothing around her, the best option she must have thought of was to give up so that her friends wouldn't continue to suffer. And after the second part, it seems like she became much more soft, she thought about giving up several times, what stopped her was her friends supporting her and reminding her to never give up. And she didn't have them at that time, because they were broken, you know?
i finished the story, a good read, i dont regret it.
However, i still dont get why girlie decided to just GIVE UP at the end fater fighting so much??