Is the questioner considered sinful for ending an illicit relationship in Ramadan, and what must he do to rectify that, especially since the girl has not forgiven him and has entered into another relationship?

It is not permissible, according to Islamic law, for there to be an emotional relationship between a man and a woman who is not his mahram; this is because it falls under taking paramours, which Islam has forbidden. Conversation with a non-mahram woman is not permissible except out of necessity, and only to the extent of that necessity, while observing Islamic guidelines. Engaging in extensive conversation without need is prohibited. Cutting off conversations in Ramadan is considered good and not reprehensible. I advise you to seek a religious and chaste girl for marriage, based on the Prophet's (peace be upon him) saying: "So win the one who is religious, and you will prosper," and his saying: "The world is an enjoyment, and the best enjoyment of the world is a righteous woman." It is not advisable to associate with a girl who has had multiple relationships.