What happens to unborn, unbaptized babies who die? If we accept that unborn babies are human beings and not merely a non-human organism, and further we require baptism as a prerequisite for salvation (using it as justification for infant baptism)...

What happens to an unborn baby which never experiences live birth, and clearly can't have been baptized since it was not yet born?

Note: I'd be especially interested (but not exclusively so) in responses to this from Catholic theologians and/or apologists.
I cannot provide a better answer then the answer provided by the LCMS (The Lutheran Church—Missouri Synod). This is taken from the LCMS FAQ: Doctrinal Issues - Baptism.
On the role of infant baptism:

Q: How does faith play a role in infant Baptism? Is faith later taken care of when the child is confirmed?
A: Lutherans believe that the Bible teaches that a person is saved by God's grace alone through faith alone in Jesus Christ. Baptism, we believe, is one of the miraculous means of grace (together with God's written and spoken Word) through which God creates the gift of faith in a person's heart. Although we do not claim to understand how this happens or how it is possible, we believe (because of what the Bible says about Baptism) that when an infant is baptized God creates faith in the heart of that infant. This faith cannot yet, of course, be expressed or articulated, yet it is real and present all the same (see, e.g., 1 Pet 3:21; Acts 2:38-39; Titus 3:5-6; Matt. 18:6; Luke 1:15; 2 Tim.3:15; Gal. 3:26-27; Rom. 6:4; Col. 2:11-12; 1 Cor. 12:13).

Summary: Lutherans believe that through infant baptism God creates faith in the heart of the infant, this faith is present though it cannot be shown outwardly.
What about unbaptized babies?

&quot;There is some basis for the hope that God has a method, not revealed to us, by which He works faith in the children of Christians dying without Baptism (Mark 10:13-16). For children of unbelievers we do not venture to hold out such hope. We are here entering the field of the unsearchable judgments of God&quot; (Romans 11:33).
What is the basis of such hope? It is this, that God is not Himself bound by the means to the use of which He has bound us. That is to say that while Christ has commanded us to baptize all nations, God can save sinners without Baptism. He did so throughout the entire Old Testament. During the first 2,000 years we know of no special means of grace for little children. At the time of Abraham He instituted circumcision, but He did not thereby provide for little girls. It is for God to determine under what conditions He will receive children into His kingdom.
A most encouraging instance for the Holy Spirit's power to influence even unborn infants in a spiritual way is found in Luke 1:15, 41, 44, where it is stated that the unborn John the Baptist leaped for joy within his mother's womb when the unborn Jesus was brought into his presence by His mother Mary. Behind all this is the all-encompassing Gospel pronouncement that &quot;God was in Christ, reconciling the world [including the little children] unto Himself&quot; (2 Cor. 5:19).
As to the second point we might say: Whether individual Lutheran pastors have ever baptized stillborn children immediately upon their arrival, we do not know, and to our knowledge such practice has never been sanctioned by our church. Nor should it be sanctioned. The means of grace, including Baptism, are for the living only (Heb. 9:27).
Usage: We urge you to contact an LCMS pastor in your area for more in-depth discussion. Published by: LCMS Church Information Center

Summary: Lutherans believe that Baptism is for the living only, however, God may have created a means to save those who were not baptized or not able to be baptized (stillborn, or died quickly and unexpectedly shortly after childbirth). This hope is based on the fact that God has shown himself capable of saving without baptism and may still continue to do so.