Your question? Yes, there is a close of probation. Just as there was with Noah's Ark, the door shut. When the Seventh Trumpet sounds it's all over: "He who is unjust, let him be unjust still. He who is righteous, let him be righteous still."

I agree they will at some point be convicted they were sinners. Why would they do this? Because this is just before their total destruction by fire. At some point they will awaken from Satan's deception to see God and all that they've lost, all the blessings in God.