Many prophetic writers make blanket statements that all children will be raptured. I do not foresee an all-inclusive rapture of every child. However, I do look for the children of Christians to be raptured because of a blessing from their parents’ faith. I recall two situations in the Bible when God blessed people because of an association. The first example is the instance when the Egyptian’s house was blessed because Joseph was his servant (Gen. 39:5) and the other example is when the house of Obededom was blessed because the Ark of the Lord remained on his property for three months (2 Sam. 6:11). The reverse of this is also true. When King David sinned, his whole house was cursed. David’s infant son died and his son Absalom rebelled against him. God himself said that He would visit judgment to the third and fourth generations for those who turn against Him (Ex. 20:5).
Ungodly parents only bring judgment to their children, so can you imagine how unsaved parents will react when they witness the rapture of Christian parents and their children while they and their children remain behind.
The two greatest biblical examples of God’s wrath being poured out on man both involved the saving of the righteous and their children. When Noah got into the ark, his children accompanied him. When Lot left Sodom, his two daughters went with him. In both cases, all of the children who remained behind perished.
Just as you work to financially support your children, your faith in God works to support your children who are under the age of accountability–in other words, until they are able to choose for themselves whom they will follow.