Alcoholics do recover. Heroin addicts recover. Oxycontin addicts recover.
Abusers don't.
Abusive men (and women) are very much like sex offenders: Their rate of recidivism is high enough that I personally would not trust one -- ever.
I've seen too many women get sucked back in by an abuser who cycles around to the sweetness and loveydoveyness again. One of them lived with me with her two kids for two weeks when I was in college because her boyfriend had tried to kill her, and she had nowhere else to go.
Remember the cycle of abuse. It always cycles back around.