Roman Catholicism has never officially endorsed the idea of Limbo (a place not as cool as heaven but much better than hell and purgatory). It was proposed as a place for children who die before being baptized and for people who believed before the Messiah's first coming. It looks as if Pope Benedict XVI is pulling the Roman Catholic church out of their ambiguity on this issue. There is no such thing as Limbo, he is now declaring.
According to the article, the idea goes back to Augustine's unwillingness to accept that God would send innocent children to hell. That, of course, fits neither with the biblical teaching on what Augustine later called original sin nor with Augustine's own views on the subject. The biblical teaching on what is required for salvation never includes a footnote indicating an exception for those under some fictional age of reason. Augustine's own views treat original sin as something that's part of us from conception, and original sin is the basis of the death sentence on every single human being (except Christ, although he faced it anyway). I can't see any absolutely compelling biblical argument against the view that all children who die young will be saved. God would have to perform a work of grace specially in each child who is saved to regenerate the person and remove the sin nature, which is what scripture teaches about every adult who is saved. But the lack of any exceptions to what seem to be clear statements seems to me to count as evidence against such a view.
However you treat the biblical silence on the issue, it's clear that there's no positive biblical evidence for such a view. The article seems to me to suggest that the reason for removing Limbo is that there's no biblical evidence for it. Why, then, assume that all children will be in heaven? That equally has no biblical evidence. Are they thinking it's better to err on the side of giving false hope in this life than it is to err on the side of preparing people for the worst in case their children who die young will not be saved?
[hat tip: Claude Mariottini]
Update: See Siris for some hesitations on a number of things here. I don't agree with his interpretation of I Peter's statement about Jesus speaking to the spirits in prison (who in context and especially in relation to Jude and II Peter's similar statements have to be the Genesis 6 fallen angels, with the message one of victory over them rather than salvation). [Update 2: See his comment on this post for his clarification even on that.] I don't have much background in the other issues he raises, but he's much more aware of the history of theology than most religion writers for newspapers like the Chicago Tribune.