There are so many reasons to that, but I'll try to list a few. I am a man, but I used to volunteer at a women's shelter to work with women who fled with their children.
The absolute, #1 reason, is that the abuser apologizes and swears it won't happen again. The abused at this point is often psychologically damaged to the point where they don't know what else to do so they accept the apology. But studies show that abusers often repeat their behaviors. It is very, very rare for women to show up at a shelter after the first time. It is usually after a pattern (years) of abuse, or a life threatening scenario.
The second biggest reason is fear. Often the person who is being abused has been threatened (sometimes with their life) to not tell anyone. That can be a terrifying experience, and results in many not reporting their abuse.
The third largest is that many abusers force their "partner" to cut off ties with friends, family, and often even quit their jobs. Emotional abuse and social exclusion is often the first step abusive partners engage in. Manipulation is part of an abusive relationship, and many people find themselves accepting the manipulation before they realize what's going on, and once the physical abuse starts they have no one left they can turn to.
Money. Often the abusive partner is the one making more income, and can simply threaten to cut off the person they are abusing. If children are involved, this makes it even more difficult of a situation. If someone is being beaten and they have children but zero income, and the person beating them says I'll stop feeding you and your child if you tell anyone, they often don't tell anyone.
Abusers use emotional abuse in another way - they make the person who is being abused feel guilty. Abusers make them feel like it is their fault they are getting beaten, and make the abused feel so bad about themselves that they accept that rationalization. Often this happens to already depressed or otherwise emotionally distraught people.
There are more reasons. But I hope this helps.