Is it a sin to continue loving and offering advice and support to a friend, knowing that she commits grave sins, repents, and then relapses, and is this love an indication of a corrupted heart?

You bear no sin for loving your disobedient friend, as long as your love for her stems from the goodness and righteousness within her, coupled with your dislike for the sins she commits. It is possible for love and hatred to coexist in one heart towards a person who combines obedience and disobedience.

Sheikh Ibn Baz says: "The believer loves for the sake of Allah and hates for the sake of Allah. If a person possesses both good and evil, like a disobedient Muslim, he is loved commensurate with his Islam and hated commensurate with his disobedience."

However, you must distance yourself from your friend if you fear harm to your faith from her companionship, or if abandoning her will deter her from sin and bring her back to obedience.