I feel like Bruce would stay in an abusive relationship because he’s in an abusive relationship with himself.
He logically knows that no one deserves to be abused in any capacity, but he may try to rationalize the fact that it’s him, so it’s fine. Or he may try to delude himself into believing that what’s happening isn’t ‘actual’ abuse and he's simply blowing it out of proportion.
The thought of Batman being abused by their partner is such a ridiculous notion. He may think that just because he is Batman, he's supposed to be able to handle anything that comes his way, or, once again, that it's not actually abuse because how can the Batman get abused?
He may even think that it’s better if it’s him going through all the pain and staying in the relationship; that way, he’s keeping people away and saving them. It's his own kind of self-sacrifice and punishment.
If they're a civilian, he thinks it's his duty to take their pain and burden himself with it. He's a hero; he has a responsibility to look out for and take care of those who cannot. It doesn't matter that the civilian is the one doing harm to him. If it's another hero, antihero, or morally gray person, he'll still feel as though it's his responsibility to take on the stress and pain of having to protect the population, and he's someone who understands the stress, so it's fine if they use him as an outlet.
As long as they don't hurt anyone else, it's fine if he gets hurt. It's his own kind of self-flagellation.
Just thinking thoughts and whatnot
