What is the ruling on refraining from visiting parents every Thursday and Friday due to distance, given that the son visits them on official holidays and invites them to visit him, but they refuse?

It is obligatory to obey parents and visit them to the extent that satisfies them, as long as it does not harm the children. If fulfilling their desire for weekly visits does not cause harm, then it is obligatory to obey them in this, even if it is difficult, because obeying parents is obligatory in matters that benefit them and do not harm the son. And honoring parents is one of the greatest acts of drawing closer to Allah, and a cause for good in this world and the hereafter.