I think it is difficult to discuss the concept of accountability without putting it into the context of other views of similar sorts, from which this concept seems to be derived from their rejection.
Basically the Baptist tradition comes from the earlier Anabaptists of history which in many ways were largely defined because they could not accept views of infant Baptism that implied the child baptized received the full measure of Christian grace as did an adult who was converted to Christ and then Baptized.
In rejecting infant baptism a security blanket was thrown aside in terms of parents and their practical concerns over their children.
Let's back up a bit. Let me explain things in terms most acceptable to a Baptist for ease of communication. First, one what might be considered the extreme end of support for infant Baptism, parents think that their child was elect and that their decision to baptize the child is only a symbolic right confirming that God chose this child to be born under the covenant of their parents, before the foundation of the world. In this sense God may also see fit to actually regenerate the infant with new birth during the actual Baptism and dedication of the child to God. This belief necessitates a wide view of the possible sins a Christian can commit because often these children go through a deep wilderness before finding God in outward profession.
A more moderate stance on infant Baptism can be seen here presented by John Owen On Infant Baptism (keep in mind Owen was a kind of Job, he had 17 kids, 16 of which died as infants with the 17th daughter also dying shortly after being married). On this stance there does not seem to be an absolute belief that every child is actually reborn in infant baptism, but there is a strong assumption of the “Age of accountability” implicit in the protected state of a child who has been baptized as an infant but this 'security' blanket is not there for the child who has not. Some difficulty is presented here because even when past writers are very clear about various aspects, the exact meaning of infant baptism seems to be partially avoided. In any case, Owen seems also to have some degree of faith in God's election as protecting children before a kind of age of accountability under the faith of their parents and he imagines the same kind of thing to occur under the Old Testament with circumcision. Owen would be the last reformer to say that circumcision still protected children once they had rejected the faith of Abraham, but there is definitely an age of protection by grace upon infants until they are old enough to be properly accountable.
The other reformed extreme is possibly presented by a person like Jonathan Edwards who in some ways was more cynical about infant Baptism then Baptists are. Edwards supported infant baptism but often indicated a belief that infants were often escorted into hell under judgments such as the fire that rained down on Sodom and Gomorrah, almost taking the reverse view of an elect protection, which he also seemed to hold, but rather a election to damnation represented by lively figures of flames engulfing children in their cribs. What can we say about that except even average Baptist would back away bit from the red-hot sermons of an Edwards. This could partly indicate why some of his congregations complained about having suicidal thoughts. But this is not about Edwards, so I digress. For an excellent survey and analysis particularly on Edwards thoughts and how they fit into historical views, read this Jonathan Edwards, Infant Baptism.
So why have I put all this history forward? Well it answers you question in a round about way. Baptists simply reject the sacrament as a means of rebirth but prefer to wait and baptize those who actually have faith. However as the security blanket that comforted parents in the old regime (the baby) was thrown out with the bathwater (pun intended) Baptists need to recreate an “Age of accountability” to infer the mystery of protection by grace according to election. I do not think there is a doctrinal basis for the belief, nor is this ‘temporary protection’ believed by all Baptists, as many are more similar to Jonathan Edwards. The problem with the idea of ‘temporary protection’, regardless of its origin, is that it is like the argument of the beard. How many whiskers make a beard? Each person has a different answer. So how old is accountable? Two months, two years, twenty years? All depends on who you ask.
I think the whole matter is better resolved in looking at Abraham willing to sacrifice Isaac. He had faith and did not need to make complicated conjectures. Have faith and dedicate your children to God. I partly feel that if the sacrament was not abused by those who claim absolute regeneration through baptism, then the Anabaptists would never have existed. Also because there are those that take false security in their child’s baptism, and so do to not make every effort to ensure their children come into the faith of the gospel. Even if God did intend that parents baptize their children as infants, God also accepts the Anabaptist practice on account of its rejection of a twisted corruption of the original.
In the end a parent who looses a child must put their faith in God. Even parents who loose their children as adults, who seem to have forsaken the way, must have 'hope against hope' or believe even when we have little supporting evidence. (Romans 4:18) The idea that our children could be in hell is to terrible to bear, regardless of whether we believe in an age of accountability, or infant Baptism, or not. Every parent shares the same concern and the same doubts that God alone to comfort us by faith. Faith does not always need logical explanation when it pertains to eternity, election, time and children.
In some ways this is one of the few subjects where I accept pretty much everyone’s views on the subject, aside from the extreme end where baptism is enough to save a child, even if he turns out reject the faith or even to become Hitler.