Whatever is not of faith is sin, so faith is the key for our children. If our children do not come to trust God there will be nothing that can be done for them. There is no obligation that could be enforced upon God in the name of love which could cause him to give eternal life (freedom) to those who do not trust him. Could God allow the evil of sin and rebellion to continue just because some of those who have faith happened to have children who did not? Not without resigning his throne as God!
The love of God is broad and deep, but its object is humans made in his image with creaturely freedom. It is important to God that our children be in his image and have creaturely freedom. Everyone made like that must come to the place where, freely, they trust God and choose to follow him. Our children must come to that place or be separated from God forever.
Perhaps we could never bear to write-off our children and would always find a way to preserve them and commune with them. We are not God. We do not see what he sees and do not have the pure moral clarity he does. God does love our children, but not with sin-stained, sentimental affection like we are apt to. He loved them enough to make them in his image and to redeem that image eternally through the sacrifice of Christ.
God wants our children with him forever, but that is not possible if they do not trust him.