**Note: I only make references to “he” as the abuser for lack of a better word, not to insinuate that only men are abusive in relationships.
Often times, the abusive person in the relationship will tell them things like, “I love you. I would never leave you, you know that? If you ever left me, I would hunt you down and…” (You get the idea).
The victim of the abuse believes the abuser, thinking that they must love them, why else would we still be in a relationship? Why would they care about them leaving him so much that he would hurt me if I left? Or they simply stay in the relationship out of fear that their abuser would follow through with their threats.
Other times, the abuser always apologizes, saying things like “I love you. I don’t know what came over me. I promise that I will do better from now on.”
Again, playing the love card, the victim believes the abuser. And they think, they love me. They will get better because he loves me. But, of course, they never do stop the abuse, yet the victim is drawn by the love that they share.
Sometimes, the abuser is the source of income and a roof over the victim’s head. If the victim leaves the abuser, they will have nothing, so they stay in the relationship.
Also, as @EmpressPixie stated, the abuser often puts down the victim to the point that they believe that they deserve their punishment. Thus, they don’t feel a need to get out of the relationship.
If the abuse involved is sexual, the abuse can make the victim feel so badly about themselves and become so ashamed that they feel they don’t deserve to live happily and without pain. They can become very weak and unstable mentally and physically, and leaving the relationship isn’t their main focus. This also occurs with physical and verbal abuse, but is much more common when sexual abuse is present.
Like I briefly mentioned earlier, fear is also often a major component. The abuser often makes threats to their significant other, so the victim becomes afraid to leave. If they outright tell their abuser that they’re leaving them, they will get hurt, so it’s usually not an option. But if they sneak out, they’re afraid that they will be caught. They assume that the abuse that will be delivered is worse than any abuse they would get otherwise.
Not to mention, some abusers are so convincing and obsessed that they will literally hunt down their victim if they leave, and deliver one final blow, which the victim knows. So these victims stay in the relationship because they figure any abuse that they would get on a day to day basis would be better than the abuse that they would get for leaving.