Thank you for posting this, and for the bump. I didn't know about the Muslim significance of Fatima.
As long as a heresy allows the heretic to better contemplate God from his unique vantage point, the heresy will persist. We do notice conversion of Muslims, not to Christianity, but to secularism. This secularization is seen, not incorrectly, by some Muslim thinkers as westernization, and we have this war on the Western civilization as a result. Why secularism brings a Muslim closer to God? Because it reminds him of the loving and forgiving nature of God, that smiles at our petty philistinism. This aspect of God is nearly completely hidden from view in Islam.
I hope that the internet will open Islamic society to Christian teaching, even classical philosophy. I know someone who corresponds with Muslims in north Africa over the internet. He told me that they frequently say things like, "We don't have to believe these things?" The idea of freely accepting or rejecting specific religious doctrines is a strange idea to them.
Another obstacle to Muslim conversions is psychological. Because the Koran contains contradictory passages, and because the Koran is treated as the literal word of God, Koranic teachings must be accepted on blind faith, and in contradiction to natural reason. So Muslims must also overcome a lifetime practice of sublimating contradictions.