There is no specific time period, but part of the answer will depend on the specific wording of the Court orders. His delay, in combination with his past history, could certainly justify going into Court and asking to change or reduce the schedule of supervised visits to something he would find more manageable. However, no Court is going to completely terminate supervised visits - and under most circumstances, it is better for the child for there to be at least some, albeit supervised, contact between parent and child. The visits will still be supervised.
It sounds to me that the wisest course would be to assess if a change in the schedule would be a good thing for your child, file a motion if need be, and in the meantime begin the intake process.
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The visitation schedule is enforceable by him until the Court says otherwise. If you have concerns that the delay makes it so that the visitation schedule is no longer in the best interests of the children then you will need to take it up with the judge - either by means of a motion or complaint for modification depending on the status of your case.
Disclaimer: This answer is provided for informational purposes only and it is not intended as legal advice. Additionally, this answer does not create an attorney-client relationship. If you wish to obtain legal advice specific to your case, please consult with a local attorney.
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