Is it permissible for the wife to postpone answering her husband's call to bed due to caring for their autistic child and waiting for him to sleep, knowing that this postponement might extend for hours or days?

A wife is not permitted to refuse her husband's bed except for a legitimate Shar'i (Islamic legal) excuse. If there is a fear that harm might befall the child if left alone, then your wife is excused in refusing until the child falls asleep. However, if it is possible to leave the child alone and there is no fear of harm to him, then she does not have the right to refuse. It is advisable for the spouses to communicate and reach an understanding to combine the husband's right to intimacy with his wife and the child's well-being and safety.