Parents of unbaptised babies need not be concerned and may trust in the mercy of God and Jesus’ love of them.
On April 22, 2007, the International Theological Commission released a document, originally commissioned by Pope John Paul II, entitled “The Hope of Salvation for Infants Who Die without Being Baptized.”[21]Pope Benedict XVI authorized publication of this document.
**“Our conclusion is that the many factors that we have considered above give serious theological and liturgical grounds for hope that unbaptized infants who die will be saved and enjoy the beatific vision. We emphasize that these are reasons for prayerful hope, rather than grounds for sure knowledge. There is much that simply has not been revealed to us.[22] We live by faith and hope in the God of mercy and love who has been revealed to us in Christ, and the Spirit moves us to pray in constant thankfulness and joy.[23]
What has been revealed to us is that the ordinary way of salvation is by the sacrament of baptism. None of the above considerations should be taken as qualifying the necessity of baptism or justifying delay in administering the sacrament. Rather, as we want to reaffirm in conclusion, they provide strong grounds for hope that God will save infants when we have not been able to do for them what we would have wished to do, namely, to baptize them into the faith and life of the Church.”
The document states that the theory of Limbo, “elaborated by theologians beginning in the Middle Ages, never entered into the dogmatic definitions of the Magisterium”**
Catechism of the Catholic Church, states that “God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments” God is free to be merciful. "