Am I sinful if I stop repeatedly forbidding my sister from an illicit phone relationship, fearing her aversion, especially with the deterioration of her psychological state, and how can I convince her to abandon this matter?

It is not permissible for a Muslim woman to be in an emotional relationship with a non-mahram man. One who does so is committing a grave sin and is in great danger. She should be prayed for guidance, because "Indeed, the hearts of all mankind are between two of the fingers of the Most Merciful, as one heart, He turns it wherever He wills." She should also be continuously advised with kindness, taking into account the appropriate times and circumstances for advice. Indeed, boycotting might be more beneficial than reconciliation if its benefit outweighs the alternative. Her guardian must be firm with her to deter her, for Allah Almighty says: "O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones."