Before answering your question – have you made this person aware that (s)he is abusive and hurtful? Many people are so self-absorbed that they actually have no clue that they are committing onaas devarim. It is a chessed and a CHIYUV d’Oraisah to give them mussar. Many of us have trouble doing so.
That said, if someone keeps consistently abusing verbally, then apologizes, my response to that is, I can only be moichel if you are sincere in your apology. In order to do teshuvah, you have to first acknowledge wrongdoing, then honestly apologize, and finally(most crucial), make a sincere plan not to do this same action again. One who sins and says he will do teshuvah and then sin again, is not forgiven by Hashem on Yom Kippur. If the Most Merciful One deems that to be unforgivable, I see no reason why we should be more forgiving than He.
Maybe (and it may be a challenge to do this) you should distance yourself from someone who is that nasty to you. Unless it is your mother or father, or someone who is mentally ill, cutting off the relationship might be best, as least in the short term. Sometimes a person needs that jolt, in order to realize how hurtful they are being. If I am talking out of my sheital, I apologize (sincerely).