The Catholic Church teaches that in order for the saving truths of the faith to be preserved, explained, or observed, Christ endowed his Church with the charism of infallibility.1
It is not uncommon to hear that the Holy Spirit will intervene directly in order to preserve the purity of faith [e.g. this YouTube video].
From Scripture, we know that God can and has saved miraculously and with an outstretched arm.
The question is, through Church history, by what evident ordinary methods [grace working in, with, and through imperfect men] has God preserved infallibility in the Catholic Church?