What is the ruling on maintaining ties with brothers and sisters who abandon prayer out of negligence and laziness, and how can one reconcile this with pleasing a mother who commands maintaining these ties, and what is the permissible limit for maintaining ties with them if it is deemed permissible?

Kinship ties must be maintained, even if the relative neglects prayer or is immoral. However, it is permissible to abandon them if that leads to their rectification. But if there is no hope that cutting ties will deter them, then maintaining kinship ties becomes obligatory in obedience to Allah's command and to please one's parents, while continuing to admonish and remind them. There is no specific duration or fixed method for maintaining kinship ties; rather, it is subject to custom and circumstances.