Yes, I've heard all that before, but your scriptures and Christian scriptures clearly state that *ALL* prayers will be answered. "Ask and it shall be given" says Matthew. Presumably you meet the conditions you said are necessary in order for prayers to be answered, you claimed you've had prayers answered, so pray for the remission of all childhood cancers, ask him to do it for its own sake and to help you prove to all the idolaters and mockers in here that you're right.
Then you can ask him to explain why nothing happened, why it was not given when you asked. I've no doubt the only explanation you'll be able to come up with will be the same retreat into incoherent mysticism ahmadabdalrhman offered: the answer was no and we can't understand that but it must be a good thing. And if that's really the answer, then we shouldn't be doing anything to relieve the suffering of the innocents either, it was ordained by god for some higher purpose that's beyond our comprehension and we shouldn't be so presumptuous as to interfere with it, let them suffer and die as god willed.
Call on God and pray Him whatever you want.
God – be exalted – said in the Quran 7: 56
وَادْعُوهُ خَوْفًا وَطَمَعًا إِنَّ رَحْمَتَ اللّهِ قَرِيبٌ مِّنَ الْمُحْسِنِينَ
The explanation:
(And call on Him
while in fear [of an enemy or a danger]
and while hoping [to have any good thing];
for the mercy of God is near to [touch] those who do charity.)
All people may pray God for a certain affair; on the other hand, one individual may pray forgiveness, grace and blessings for all believers.
God answers the praying of one who prays and supplicates Him, unless such a man is a disbeliever, atheist or associater.
This is in the Quran 13: 14
لَهُ دَعْوَةُ الْحَقِّ وَالَّذِينَ يَدْعُونَ مِن دُونِهِ لاَ يَسْتَجِيبُونَ لَهُم بِشَيْءٍ إِلاَّ كَبَاسِطِ كَفَّيْهِ إِلَى الْمَاء لِيَبْلُغَ فَاهُ وَمَا هُوَ بِبَالِغِهِ وَمَا دُعَاء الْكَافِرِينَ إِلاَّ فِي ضَلاَلٍ
The explanation:
(His [preaching] is the preaching of truth;
but those who call to other than Him, they answer them not at all save as one [soul] who stretches out his hands to the water that it may reach his [spiritual] mouth, but it reaches it not; for the praying of unbelievers is only in missing [of the truth, and their prayer will not be answered.] )
So (His [preaching] is the preaching of truth): means:
Whoever invites people to serve God alone, then his invitation is a message of truth: he is truthful, and he is more worthy to be followed; and even when he prays God, God will answer his prayer.
Certainly I may pray God to cure all the children with cancer, and He may answer my prayer; but this will be a tremendous thing: it will be a miracle like the miracles given to Jesus Christ to prove his apostle-hood: like curing the leper, the congenitally blind and the paralyzed.
Such a miracle is given to prophets; but I am not a prophet.
Not all my prayers are granted to me, but God Most Gracious answered many of my requests, and praise and gratitude is due to Him.
Of course I ask God's mercy and grace to all the innocent children; all of us pray for God's forgiveness and blessings to all believers: the ancient and the contemporary; as in the Quran 59: 10
رَبَّنَا اغْفِرْ لَنَا وَلِإِخْوَانِنَا الَّذِينَ سَبَقُونَا بِالْإِيمَانِ وَلَا تَجْعَلْ فِي قُلُوبِنَا غِلًّا لِّلَّذِينَ آمَنُوا رَبَّنَا إِنَّكَ رَؤُوفٌ رَّحِيمٌ
The explanation:
(Our Lord, forgive us and our brethren who were before us in the faith, and place not in our hearts any rancor toward the believers. Our Lord, surely You are Most Kind [and] Most Merciful.)