It seems to me, the moment when the faith to do miraculous feats arises is similar to that which leads to salvation. Although not strictly necessary (remember the Centurion), for the most part, I think it also requires the assistance of God to distill. Also like that moment, the final disposition of the aimed at goal must come through us, not God. There is nothing irresistible about the grace that stirs true faith into being.
Now there is a charismatic gift of faith through which faith is inspired in an individual for the benefit of the body. That occurs for a specific purpose at a particular time--it is not ongoing, which is the intrinsic nature of a manifestation (phanerosis) of the Spirit. Like anything else the Spirit inspires, it is quenchable. We are not puppets in the hand of God, after all, that would insult the one in whose image we are made.
I once had a Bible college professor, Bill Crew I think it was, who posited that a gift of faith came with along with any other manifestation of the Spirit. His idea was that the faith to act came along with the ability to act under the inspiration of the Holy Spirit. I don't think that is so (it's too speculative without the backing of scripture), but I do think that the stirring of the Spirit that alerts us to the moving of the Spirit is itself a grace-filled invitation to believe. It's that tap on the shoulder we need to get out beyond ourselves and get on the same page with God.
When the breath of God is exhaled across the face of the inner man a moment arises--a moment which awakens faith and calls us to possibilities of moving as the hand of God bringing the miraculous.