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Answer:
This tragic event is addressed in 2 Samuel 12. Scripture explains this phenomena as the iniquity of the fathers being visited upon their children to the third or fourth generation (e.g., Exod. 34:7; Num. 14:18; Deut. 5:9). Scripture also says that the conduct of good parents redounds to the thousandth generation (Exod. 20:4-6). We see the former played out in modern times when children who grow up fatherless because of a delinquent father, or who grow up with an abusive father, tend to suffer more than those who are spared such an upbringing. Similarly for children whose mothers are drug addicts, as they are more likely to be harmed by birth defects.
These are the sad consequences of free will exercised badly.
Regarding David and Bathsheba, they are to blame for the child’s death, not God. Similarly, by virtue of original sin, every merely human child, save for the Blessed Mother, is subject to the contraction of original sin, the preeminent way in which the sins of the father (Adam) are visited upon their offspring (see CCC 404). So it is not unjust for death to be visited them by God (see Rom. 6:23).
Finally, just because a child like David and Bathsheba’s dies in infancy doesn’t mean God has abandoned them. Death doesn’t have the last word with God, and the early death of David and Bathsheba’s child—as with the deaths of Egyptian firstborn just prior to Israel’s exodus—does not necessarily portend their eternal destiny. We commend them all to God’s mercy, and we heartened by Scripture that God sent his only divine Son because he loves and wants to save us all (John 3:16-17, 1 Tim. 2:4, 2 Pet. 3:9).