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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)

I don't recognize your assumptions as Scriptural. Instead I find in the Bible that man is incapable of doing anything righteous, and that true faith, once given, is non-refundable because it's predicated on God's plan for His creation. It's His call.

Either we have been redeemed by Christ's atonement alone or we haven't.

"And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
And for this cause God shall send them strong delusion, that they should believe a lie:
That they all might be damned who believed not the truth, but had pleasure in unrighteousness.
But we are bound to give thanks alway to God for you, brethren beloved of the Lord, because God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth " -- 2 Thessalonians 2:10-13

"Chosen to believe."