She's protecting her father. Even in abusive situations, there is often a co-dependent relationship between a father and a daughter. Here it seems there might be even more of a relationship with a missing mother and the father's need for a female in the home (in more than one way possibly).
If she struggles with her father, she may indeed be a character who would want to remain in that abusive situation just to protect the other children from him. They are younger and need some kind of a care-taker.
Think about the racial dynamics of those days and think about what her father is like...
One of the reasons that Tom is in so much trouble is that black men and white women are not supposed to have anything to do with each other in that time and place. So if Mayella has been voluntarily doing something even a bit physical with a black man, she will be totally scorned and shunned by other whites.
In addition, her dad is a pretty violent man. If he feels like she has humiliated him, he will surely beat her.