It is sometimes charged that Calvin taught the actual damnation of some of those who die in infancy. A careful examination of his writings, however, does not bear out that charge. He explicitly taught that some of the elect die in infancy and that they are saved as infants. He also taught that there were reprobate infants; for he held that reprobation as well as election was eternal, and that the non-elect come into this life reprobate. But nowhere did he teach that the reprobate die and are lost as infants. He of course rejected the Pelagian view which denied original sin and grounded the salvation of those who die in infancy on their supposed innocence and sinlessness. Calvin's views in this respect have been quite thoroughly investigated by Dr. R. A. Webb and his findings are summarized in the following paragraph: "Calvin teaches that all the reprobate 'procure' — (that is his own word) — 'procure' their own destruction; and they procure their destruction by their own personal and conscious acts of 'impiety,' 'wickedness,' and 'rebellion.' Now reprobate infants, though guilty of original sin and under condemnation, cannot, while they are infants, thus 'procure' their own destruction by their personal acts of impiety, wickedness, and rebellion. They must, therefore, live to the years of moral responsibility in order to perpetrate the acts of impiety, wickedness and rebellion, which Calvin defines as the mode through which they procure their destruction. While, therefore, Calvin teaches that there are reprobate infants, and that these will be finally lost, he nowhere teaches that they will be lost as infants, and while they are infants; but, on the contrary, he declares that all the reprobate 'procure' their own destruction by personal acts of impiety, wickedness and rebellion. Consequently, his own reasoning compels him to hold (to be consistent with himself), that no reprobate child can die in infancy; but all such must live to the age of moral accountability, and translate original sin into actual sin." 37As typical of a book from Boettner, the reference is vague. In this instance though, through the help of Google, "Calvin Memorial Address" by Dr. R.A. Webb is available: Calvin's doctrine of Infant Salvation. Dr. Webb points out that the information on Calvin's view is controversial, in that various extracts from his writings are marshaled together to indict him of teaching certain infants dying in infancy are damned. He goes through a number of these quotes. Webb argues as Boettner summarized above. Webb's form of argument appears to me to be similar to those who argue Calvin held to a limited atonement. That is, without direct and lengthy statements from Calvin on a particular issue, his position is arrived at by evaluating controversial or vague quotes, and then plugging them into his system.
37. Calvin Memorial Addresses, p. 112.
What interested me about Webb is that if he's correct, Calvin in essence taught a form of the age of accountability. While I can think of a few specific Reformed theologians that held (or hold) a type of "age of accountability," I'm not familiar with any major Reformed confession teaching it. The popular notion of an "age of accountability" is more of an Arminian concept- that children reach a particular age in which they are culpable for their sins. That is, if they haven't accepted Jesus Christ (or even heard of him) before this particular age, and if they die before that particular age, they go to heaven. I've often wondered why Arminian parents would ever want to take the chance of allowing their child to reach the age of accountability and risk having that child potentially lost for eternity.