The story of the Prodigal makes perfect sense IF one recognizes that not all are legitimate children of God.

Any human being born in history is a child of God. God is father to all, not just a select few.

The Prodigal was always a legitimate son, and because of that, could not fall away.

You are absolutely reading the story incorrectly. It has nothing to do with being unable to lose your salvation, and has everything to do with God's infinite and unfathomable mercy.

There ARE illegitimate sons, and they are never saved.

Nowhere does the Bible teach that. However, the Koran surely does.

Please note the words of the Father to the elder son, "All that I have is yours". That shows the loss of the junior, but his salvation was never in question.

It shows nothing of the sort.