“That is that infants who die without baptism go to a place of natural happiness, but are deprived of the Beatific Vision (actual presence before God in Heaven). This state is commonly known as “Limbo.”
I have a hard time with that theory when David says “He cannot come to me but I will go to him”. But as sandyeggo said, “the Church can only entrust them to the mercy of God,”.
I grant that the area is a difficult one. In the end, only God knows, and we won’t find out till after our own individual deaths.
That's certainly your prerogative. Though one thing that may make it easier to believe is thinking of where Abraham and the other patriarchs were before Christ opened heaven. The "bosom of Abraham" is traditionally thought of as a kind of limbo.
Granted, it's a different case than we're discussing here, but at least it shows that the idea of a kind of middle place is not alien to Christianity.