If someone wrongs me and doesn’t repent, am I obligated to forgive them?
Jesus commands us to forgive ON THE CONDITION OF repentance (Lk. 17:3-4). Even if the wrongs are continually done and yet are still continually accompanied by repentance, forgiveness is required. This would also mean that forgiveness would not be required if the wrongdoer does not repent. After all, God himself has never forgiven anyone who has not first repented.
That said, it must also be pointed out that God shows love and kindness even to those who are unrepentantly evil (Matt. 5:44-45). We are called to be like him in every way (Matt. 5:46-48).
So we should not think, “Ah, he has wronged me and he has not repented! That means I don’t have to forgive him! And THAT means I am allowed to hate him and treat him terribly!” No, even without forgiving them we are still required to love our enemies, bless them, and be kind to them (Matt. 5:44). After all, that’s what God did to you when you were still his enemy. Aren’t you glad he offered you his hand even while you were still in your sins? (Rom. 5:6-8)?