Some things in Scripture need to be set in their immediate context and others require the whole backdrop of God's revelation in order to unpack them fully.
Hear, O heavens, and give ear, O earth: for the LORD hath spoken, I have nourished and brought up children, and they have rebelled against me. The ox knoweth his owner, and the ass his master's crib: but Israel doth not know, my people doth not consider. Ah sinful nation, a people laden with iniquity, a seed of evildoers, children that are corrupters: they have forsaken the LORD, they have provoked the Holy One of Israel unto anger, they are gone away backward. - Isaiah 1:2-4
The reason that this is astonishing, the reason that it indicates the iniquity of the people and incurs the Lord's anger is precisely that it goes against what is intended in child-rearing. The parent should carefully direct the child along right paths of thought and behavior and the child should honor father and mother by an attitude of 'trainability'.
The Proverb 22:6 "Train up a child in the way he should go: and when he is old, he will not depart from it." is a succinct description of the how the child-rearing process is supposed to work. It is not so much a specific, individual promise as it is the path tending toward blessing and success in this particular endeavor.
While the Proverb in question does not contain a clear contraindication such as "A prudent man foreseeth the evil, and hideth himself: but the simple pass on, and are punished." it does set itself against a very common biblical rebuke toward those who will not discipline their children:
He that spareth his rod hateth his son: but he that loveth him chasteneth him betimes. - Proverbs 13:24
And, indeed, the training up of a child in the way that he should go must include such chastening, such sparing not of the rod of discipline. The reason this process is necessary is because of the child's sinful nature, that human disposition tending toward rebellion.
I believe that, if one looks at the biblical history of the nation of Israel one may quite clearly discern the chastening of the Lord as He trains up His children in the way that they should go. Later, as the New Covenant unfolds, we begin to see that not every individual person is a child of God by nature. We begin to see that:
they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed. - Romans 9:6-8
In this way, the repeated and deepening rebellion not only of Israel but of all humanity and the resultant chastening from God should not be seen as a failure of Proverbs 22:6 but as a demonstration of the process laid out in that Proverb.
Those who are truly God's children, who are of the faith of Abraham and have been 'begotten again unto a lively hope by the resurrection of Jesus Christ from the dead', and who are 'elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ' these will not depart from the way they should go when they are old. Indeed, they are told that He who has begun a good work in them will bring it to completion at the day of Christ Jesus. For God, the process of the Proverb does not fail.
And if the Proverb is to be looked at from a merely human point of view, certainly common sense tells us that to leave a child completely untrained is a recipe for disaster and certainly experience has taught us that poor or inconsistent training brings similarly poor results ... in general.
- Note: Young's Literal Translation renders the verse like this: "Give instruction to a youth about his way, Even when he is old he turneth not from it." Read like this it seems to say less about the content of the training and to be more of a declaration that child training produces results that are not turned away from regardless of whether the training is good or bad. Read like this it could be an explanation of how the sins of the fathers are passed along to the succeeding generations: No human parent is perfect, therefore no child will be trained perfectly.