We usually associate the love of God with the benefits we receive from him and the blessings that come from his kind and merciful hand. Because his love usually manifests itself in good things that happen to us, we sometimes fall back in shock and consternation when we see a child struck by disease or some other trauma.
Before we speak to the question of why God allows children to suffer, we need to ask the bigger question: Why does God allow suffering to happen to any person, whether he's two years old, two months old, or twenty years old? The Scriptures tell us that suffering came into the world as a consequence of the fall of man and of creation; that is to say, it is because of sin that God has visited judgment upon this planet. That includes the curses of pain, disease, sorrow, and death that attend the consequences of wickedness.
How could a loving and holy God allow a baby to suffer a debilitating disease? I think the answer is partly contained in that very question. God is holy, and in his holiness he exercises judgment against the wickedness that is prevalent in human nature. When we ask the question with respect to infants, sometimes lurking behind that question is the unspoken assumption that babies are innocent. Virtually every church in the history of Christendom has had to develop some concept of what we call original sin because the Scriptures teach us so clearly that we are born in a sinful state and that the curse of the Fall attends every human life. That sounds grim and dreadful until we realize that in that judgment on fallen humanity comes also the tempering of God's wrath with mercy and grace and his whole work of redemption. We believe with great joyous anticipation that there is a special measure of grace God has reserved for those who die in infancy. Jesus said, "Suffer the little children to come unto me, for to such belongs the kingdom of God."
One warning that I have to raise at this point is that we dare not jump to the conclusion that an individual person's particular disease or affliction is a direct result of some particular sin. That may not be the case at all. As humans, all of us must participate in the broad complex of the fallenness of our humanity, which includes the tragedy of disease.