What is the sufficient amount of communication with the divorced father to waive the right of honoring him?

The right of the father is immense and is not forfeited by his harshness or by his ceasing to inquire about you. You must honor him and treat him kindly by contacting him, visiting him, and providing him with every possible good. You must strive to understand the reason for his harshness and remove it, exercising patience in this regard and seeking Allah's help. For honoring one's parents is among the greatest reasons for Allah's pleasure and entry into Paradise. "The Lord's pleasure is in the parent's pleasure, and the Lord's displeasure is in the parent's displeasure." And, "The parent is the middle gate of Paradise; so if you wish, you may neglect this gate or preserve it."