The children of believing parents are "holy," meaning "set apart." God considers such a child to be "clean." That does not mean "sinless," but they are still legally clean in His sight. They are therefore acceptable in His presence and have the opportunity to have true success in life as a result. They have the chance to believe God, to cast their lot with Him, and to be spared the horror of having to face many of the evils in this world.
But, just as parents can lose their sanctification, so children who are set apart can also lose their status. Law plays no favorites. It does not care whether one is male or female, or thirteen, nineteen, or ninety-three. If a ninety-three year old male jumps off the 80th floor of the Empire State Building, which direction will he go? What if a 16-year old girl does the same thing? The law of gravity does not play favorites.
Law does not care what one's race, sex, or age are. If parents who are sanctified break the laws of God persistently, they will lose their sanctification. If a seventeen-year-old does the same thing, even though his parents are sanctified and a child is held to be clean because of God's judgment, he can lose his too.
For a child who is sanctified, even though unconverted, there is still a great deal that he will be held accountable for. "To whom much is given, much is also required." Jesus does not say that this only applies to converted parents.
The child's sanctification gives him the advantage of access to God. Because of that access, he has the guidance of God available to him, and from that guidance he can form a proper vision of what he wants to do with his life (Proverbs 29:18). This allows him to see what he wants to do in terms of conduct—what he wants to pursue, the way he wants to do work, the attitude he has toward other people, parents, neighbors, fellow-employees, etc.
We can tell from the conduct of people in this world that they do not have this guidance. But a sanctifed child has access to the knowledge of what God expects, and from that he can make it his goal in life to act that way. He can set his will to do the right thing. He is sanctified, and divine guidance is what he gains from it.
He has access to truth. Even if his parents fail to give it to him directly, every Sabbath that he attends church services he is receiving it through one of God's ministers. It is available, but he still must make choices. He must discipline himself to follow the information, the true knowledge, given to him. The advantage lies in the fact that he has access to truth about the way life is to be conducted and how he can please God. He can do it because he is not cut off from God. His lamp is not put out (Proverbs 20:20).