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Gray, the "Limbo of the Just" in the Old Testament is ended, since it's purpose was for OT holy persons to wait for Christ to open the gates of heaven.

The new testament Limbo is the highest/upper part of hell (as is purgatory).  While purgatory is a state of purification, Limbo is state of natural happiness.

In God's mercy, some babies are sent to Limbo due to dying young and without baptism.  God foresaw (as only He can do) that had they been baptized and lived an adult life, they would not have saved their soul.  So, in his mercy, he hears the prayers of their parents/family and sends them to Limbo, which is infinitely better than hell.

That last paragraph is important.  Now one criticism the anti-BoDers get is that we deny God's will to save all people, and that everyone must have the active concrete opportunity to be saved.  So I always ask about the unbaptized infants.  What about them?  I always get crickets in reponse.  Then I explain as you did that God's Mercy made it so they ended up in a place of perfect happiness because foresaw that if they had received the gift of faith they would have been damned and would suffer forever in Hell.

I have once read someone claiming that God could infuse them reason and reveal Himself to them at the last moment before their death, making it possible for them to receive BoD. I don't know if it works.

Well that's a speculation, rooted in emotion, that runs counter to a long Tradition in the Church, and repeated Magisterial teachings that the only hope for infants to be saved is actual reception of the Sacrament of Baptism.  Cajetan held that theory, where the infants could be saved by VICARIOUS desire (of parents or godparents), but St. Pius V ordered that opinion stricken from his works.  Even the, why would God allow some infants who died without Baptism who vicariously saved them by their desire but other infants not to have such parents?

There's no requirement for God to present some choice to an infant before death, and, as mentioned, the Patristic and Magisterial Tradition strongly militates against this view.  In fact, if this were the case, there couldn't possibly be a  Limbo of Infants at all, a possibility which the Church largely endorsed, since everyone would then make a choice for or against God before dying.

But the bottom line, if it's permissible to hold there's such a thing as Limbo, then it's not inherently incompatible with God's will that all be saved for some to be deprived of the actual grace for conversion.  God WOULD certainly offer the grace of He foresaw that the soul would accept it and then be saved, but foreseeing that the soul would reject it, God in His Mercy permits them to have PERFECT natural happiness rather than an eternity in Hell.  Imagine every possible joy one could have, on this eternal vacation with no more pain or suffering or sickness or any affliction of any sort, but perfect natural bliss ... that's actually what MOST peole envision Heaven to be, one long extended enjoyable vacation, and none of us can even begin to imagine the actual Beatific Vision, since our minds are naturally incapable of conceiving of it.

It's for that reason that I hold there to be a huge surge in abortions, with 73 million per year worldwide, every year now for many decades.  We're approaching quickly a billion aborted infants ... and they will all enjoy perfect natural happiness forever.  What a great Mercy from God ... because in this wicked, corrupt world, especially if you were to be born to and raised by parents who would think nothing of murdering you, your chances for salvation are slim to none anyway, so the less a chance people have of being saved, the more you'll see them being aborted and going to Limbo for eternity ... where they will praise God in perfect bliss for His Mercy through all eternity.