Usually, I stop a novel if I find too great faults with characterisation, or if something happens that quite severely throws off what the story was about.
The first makes me stop being interested in a character if they can't even be one. They do things I don't think sane people do, they behave differently from how the situation they are in demands, or treat other characters weirdly, or worse, not like characters.
The second makes me lose interest in the story. I almost stopped my favorite novel, because the following happened. So the character is in a huge debt. That's a big plot point that defines a lot of her motivations, while she also has to handle accumulating power, knowledge, and a criminal investigation. So now, she gets captured by the elite police force, while being in disguise. Yet then they realize to a degree who they got. They put her in a special cell, place guards in front, and wait for reinforcements. So what happens next? She simply threatens the two guards with her reputation as an all-powerful monster, the guards help her escape, kill their comrades for a promised reward, and free her associates. Also, she stumbles on their gold treasury. To me, even though the whole novel was to me absolutely outstanding, this one bullshit chapter had so much long-lasting convenience, I almost stopped the story right there.
So yeah, this is the kind of event that puts me off.