Well with sufficient prayers for baptism of their child even in the case of miscarriage God can intervene.
So for Christian parents, properly taught of the necessity of baptism, there is this hope.
It would be a fallback existing alongside Limbo, rather than doing away with it as some would have done, which is frankly, against the writings of the saints and Revelations of Our Lord Himself.
Generally however, they should be taught as in the paper here:http://saintsworks.net/Papers%20and%20Information.htm
"How to Baptize in the Case of Miscarriage"
Something which I read is supposed to be standard Catholic teaching for parents.
Which is why I always hope that people will spread the information to other parents.
From the Revelations of St. Bridget:
'First question: Again he appeared on his ladder as before, saying: ”O Judge, I ask you: Why does one infant emerge alive from the mother's womb and obtain baptism, while another, having received a soul, dies in the mother's belly?”
Answer to the first question. The Judge answered: ”Friend, your inquiries are not made out of love but are made through my permission. So I answer you through the likeness of words.
You ask why one infant dies in the mother's belly while another emerges alive. There is a reason. All the strength of the child's body comes, of course, from the seed of its father and mother; however, if it is conceived without due strength, because of some weakness of its father or mother, it dies quickly. As a result of the negligence or carelessness of the parents as well as of my divine justice, many times it happens that what was joined together comes apart quickly.
Yet a soul is not brought to the harshest punishment for this reason, however little time it had for giving life to the body, but, rather, it comes to the mercy that is known to me. Just as the sun shining into a house is not seen as it is in its beauty - only those who look into the sky see its rays - so too the souls of such children, though they do not see my face for lack of baptism, are nevertheless closer to my mercy than to punishment, but not in the same way as my elect.'
And then Pope Sixtus V:
'For who would not detest a crime as execrable as this — a crime whose consequence is that not just bodies, but — still worse! — even souls, are, as it were, cast away? The soul of the unborn infant bears the imprint of God's image! It is a soul for whose redemption Christ our Lord shed His precious blood, a soul capable of eternal blessedness and destined for the company of angels! Who, therefore, would not condemn and punish with the utmost severity the desecration committed by one who has excluded such a soul from the blessed vision of God? Such a one has done all he or she could possibly have done to prevent this soul from reaching the place prepared for it in heaven, and has deprived God of the service of this His own creature.'
I think Clare your statement:
"The idea that unbaptised infants who die are given a chance to accept God is nice. But it means they may also reject Him. In which case they would go to the fiery part of Hell, rather than the outskirts which are more pleasant."
Is very strikingly and reminds me of some of what I have read in the past, but do not have sufficient information on.