But faith, like all gifts, is given by God.
Agreed.
But faith, like all gifts can be rejected as well as received.
God has given all men enough faith to seek God (Rom.1) and to believe the Gospel when they hear it.
It is they who must use that faith correctly.
That becomes the issue of the will.
No different then a Christian who sins after he is saved, he is resisting the grace of God (Rom.7, Eph.4, 1Thess.5)