Answer: Sometimes people are saved by miracles, and sometimes not. The ways of God are beyond us, but I do agree that the suffering of children is the most spiritually challenging form of evil in the world.
The death of children like the one you mention from incurable diseases is terrible, but it's a fact of our biological fragility that people of all ages succumb to disease. However, the death of children from avoidable and savage cruelty, such as during the Holocaust, is morally and spiritually numbing.
If I were an atheist, I would certainly use the murder of children as my checkmate move — even though, ultimately, I don't think it succeeds.
What I would humbly suggest is that our agony in the face of all suffering, particularly that of the young, comes from an understandable but incorrect and scripturally unsupported belief. Contrary to the teaching of Scripture, God does not promise us all a long and untroubled life on Earth.
God promises all of us a life accompanied always by God's love. God promises us a consoling partner as we live through life's troubles, and eternal life after death in heaven.
I understand that it's easier to believe only in a God who gives us our lives and blessings, and not also in the God who will reclaim those lives and blessings some day. I try to believe in God's giving and taking equally, and I pray that you might do the same. Justice for the evildoers among us is our responsibility. Eternal, unconditional love is God's responsibility and remains God's only and best gift.
I know a story told by the Jewish philosopher Abraham Joshua Heschel. He said that the first time he heard the story of the sacrifice of Isaac (Genesis 22) read in the synagogue, he cried.
His father asked why he was crying and he answered, "I'm worried that the angel will be too late to stop Abraham."