When the Scripture is seemingly silent on any particular topic that is of concern to the Christian church generally, there is a temptation to wonder why God was not "clearer" concerning this or that issue or question. When this occurs, a better course of action is to remember that while the Scripture is very specific on some things, a great deal of its content comes to us in the form of general principles which God expects us to apply to existential situations, questions, and decisions.
For example, nowhere in Scripture can we find a prohibition against abortion. We are not therefore free to conclude that abortion is perfectly acceptable to God. On the contrary, we take the clearly understood principles in the Scripture, such as the infinite worth of every human life, whether in the womb or out of the womb, and we apply those principles to the issue at hand. Christians can and should be guided in their thinking by those passages which underscore the sanctity of life, as they press their case in the dialog with people who are pro-choice.
Another example would be the tobacco habit. Scripture does not specifically forbid smoking. It does, however, teach us that our bodies are given to us by God and that we are to be good stewards of them. Moreover, the body of each believer in Christ is a temple of the Holy Spirit who indwells him or her. Just as sexual immorality is associated with a host of sexually transmitted diseases, some of which are incurable and even fatal (e.g., AIDS), and all of which, by the way, are prohibited in Scripture, so too the tobacco habit is associated with a host of avoidable diseases, all of which can shorten our lives unnecessarily. Again, smoking is a stewardship issue and a sanctity of life issue. The same principle could apply to gluttony, illegal drugs and alcohol abuse, texting while driving, and on and on and on.
In His teaching, Jesus never spoke of an "age of accountability" (AOA) per se. While I cannot speak to the traditions of various denominations in regard to the AOA, I can, however, suggest we use a well respected method of interpretation, by which we take the principles which are clearly taught in the Scripture and apply them to what is not so clear. This approach is a common interpretive method applicable to virtually any writing, from the Bible to a modern-day parking ticket, and it is particularly invaluable when the Bible is seemingly silent on an important issue.
In short, Jesus was silent on AOA. He did, however, have a great deal to say about children, infants, and "little ones" (who generally were not children at all, but a term for His followers). As we take these teachings, glean important principles from them, and then apply these principles to the issue of AOA, we begin to realize the Scripture is not as silent as we first thought it to be.
Over and over again Jesus stressed the necessity of coming to God as a little child, and to do so in simple, childlike faith. "Jesus loves the little children," we used to sing in Sunday school. "Red and yellow, black and white, they are precious in His sight. Jesus loves the little children of the world."
When His disciples sought to keep the little babies and ankle-biters away from our Lord, He rebuked His disciples, saying,
"Suffer the little children to come unto me, and forbid them not, for of such is the kingdom of heaven" (Matthew 19:14).
In order to capture the context and flow of the passages from which this famous verse comes, I'll reproduce here Orville E. Daniel's A Harmony of the Four Gospels (p.182) so that by conflating the accounts of Matthew, Mark, and Luke, each unique detail of the narrative from each of the Synoptics is included:
The little children were brought to Jesus for him to place his hands on them and pray for them. People were also bringing babies to Jesus to have him touch them. When the disciples saw this, they rebuked them. When Jesus saw this, he was indignant. He called the little children to him and said, "Let the little children come to me, and do not hinder them, for the kingdom of God belongs to such as these. I tell you the truth, anyone who will not receive the kingdom of God like a little child will never enter it." And he took the children in his arms, put his hands on them and blessed them (Ma 19:13-15; Mk 10:13-16; Lk 18:15-17).
Jesus was indignant that His disciples wanted to shoo away the children and the parents who had brought their babies to Him. To be indignant is to have a feeling that something is not right, that an attitude or a behavior is not worthy of a laudable value or a preferable standard for attitudes and behaviors (indignity coming from the Latin stem stem dignus, worthy + in, not) . To Jesus, the attitude that children are somehow unworthy of His ministrations was antithetical to, and unworthy of, the principles by which He lived. Hence, Jesus felt indignant.
Why were children so important to Jesus that He would encourage them to come to Him, that He would take them in His arms and bless them, that He would pray for them, and that He would use them as illustrations of important biblical principles? I suggest it was not because children are pure, innocent, and without sin; rather, it was because children almost instinctively trust their elders through a three-step process which Spurgeon used to define faith: faith begins with knowing, it proceeds to believing, and it culminates in trusting. In the same manner adults must exercise faith in a knowing, believing, and trusting process. Otherwise, we will never experience God's forgiveness, cleansing, and God's acceptance of us into His forever-family.
Trusting does not require a great deal of smarts, which is why Jesus thanked His Father that His teachings were revealed not to the wise and the intelligent, but to "infants" (see Matthew 10:25; Luke 10:21). In the context of these two verses, Jesus was thanking His Father primarily for His "infant" disciples. At the same time, however, Jesus was also underscoring the importance of exercising simple, childlike trust in God, as opposed to the relative unimportance of using worldly intelligence and wisdom to come to God (see 1 Corinthians 1:18-25).
So, then, Jesus did not speak of an "age of accountability," but He clearly valued children and used them as an example when He taught His followers on the importance of trust and humility in being converted. Children, according to Jesus, already have the requisite and sufficient trust and humility to be considered part of the kingdom of heaven. If we as adults do not become like them, we'll never be converted, and thus we will never enter the kingdom of heaven.
"'Truly I say to you, unless you are converted and become like children, you will not enter the kingdom of heaven. Whoever then humbles himself as this child, he is the greatest in the kingdom of heaven'" (Matthew 18:3,4).
In conclusion, had Jesus expected children to repent and be converted, He would have addressed them as He did His adult audience. Clearly, however, He did not do that, not even on one occasion. Since Jesus clearly loved the children and used them as an example of the values of humility and trust, we can safely conclude that children are part of God's forever family.
Sometimes when the Scripture is seemingly silent on an issue, that silence, if it is truly there, is there because God did not deem it necessary to provide more guidance than what is already in His Word in the form of guiding principles. As for the specifics of what age is the age of accountability, we need to apply those principles on a case-by-case basis, just as God will in the day of judgment.