How do Christians who reject the idea of purgatory deal with the fact that most people don't repent of every sin before they die?

When God saves you from sin, he saves you from sin.

Simply put, in Protestant theology, God doesn't save you from some of your sins. He saves you from all your sins. You aren't saved through works, but through the divine grace of God. The works (including acts of repentance) are the result of being saved, not the cause of it. All God requires of you is to have faith in Him, and to at least make a good faith effort at trying to be a good person.

Perfect love casts out fear.

Hereby know we that we dwell in him, and he in us, because he hath given us of his Spirit. And we have seen and do testify that the Father sent the Son to be the Saviour of the world. Whosoever shall confess that Jesus is the Son of God, God dwelleth in him, and he in God. And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him. Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world. There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love. We love him, because he first loved us. - 1 John 4:13-19

Our boldness in approaching God in thanksgiving, prayer and supplication; our boldness in considering and facing the day of judgement (which will surely come upon all men) hinges not upon achieving and maintaining some threshold of behavior. We are not welcomed into God's presence based upon our works or as the result of an accurate accounting and commensurate repenting of each and every individual sin (which we cannot accomplish because our hearts are deceitful and wicked (Jeremiah 17:9-10)) but upon His work which He worked in Christ from the foundation of the world.

Our boldness results from:

• our current residence which we enter by confessing that the Father sent the Son to be the savior of the world. Whoever confesses that Jesus is the Son of God dwells in God and God dwell in him.
• confessing (and believing) that Jesus is the Son of God, we are given the Spirit (variously called of God, of Truth, of Christ, etc.) by which we know that we dwell in Him.
• being made (by the indwelling Spirit) into the image of Christ in love as He is (in God's love) so are we in this world (in God's love).
• fear being cast out by the perfect love of God in which we live and which lives within us. Fear has torment and God has not sent His Son to torment us.
• the clear understanding that we have not earned God's love. God's redeeming work is from before the dawn of creation. Our love for God is a gift from God empowered by God.

And hope maketh not ashamed; because the love of God is shed abroad in our hearts by the Holy Ghost which is given unto us. For when we were yet without strength, in due time Christ died for the ungodly. For scarcely for a righteous man will one die: yet peradventure for a good man some would even dare to die. But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. Much more then, being now justified by his blood, we shall be saved from wrath through him. For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life. - Romans 5:5-10

It is oft repeated (and wrongly) that, while Christ died to justify sinners, it lies upon us to overcome, as though God has done His part and it is up to us to do our part. And surely Jesus promised (in Scripture) "To him who overcomes I will..." but it is our flesh which desires to overcome by our own works. This is the man-made religiosity of self-justification. We wish to deserve, to pay back, to earn the free gift of God, but who shall stand before God and demand what we have earned. This is the fountainhead of fear.

What does the Scripture say about those who overcome? First, we have overcome the wicked one (1 John 2:14): it is past tense. Second, our overcoming is not by works but through a new birth by the believing of faith (1 John 5:4-5), Third, we overcome by the blood of the Lamb, the word of our testimony, and the loving of truth above life (Revelation 12:11).

Having begun in the Spirit we must not, we cannot, be made perfect in the flesh. The fear of God is the beginning of wisdom not the goal. The Gospel is God's gracious gift of love whereby He demonstrates and satisfies the inherent requirements of His own perfect righteousness in His Son. Purgatory is the illegitimate offspring of fear and pride of life: One fears God enough to realize one falls short and yet will not abandon one's own works and rest all upon Christ.

One who suspects that they may spend time in a purgatorial state does not yet have full confidence (or perhaps no experience yet at all) in the love of God which is in Christ Jesus.

Whatsoever is not of faith, is sin. [Romans 14:23 KJV.]

All that believe are justified from all things [Acts 13:39 KJV.]

The question about purgatory can be answered by concentrating on justification by faith. If justification by faith be true, there is no need for a state (called 'purgatory') which is not mentioned in the bible.)

The question posits that what it terms 'repentance' and 'confession' is necessary to apply to each single sin, in order for each single sin to be 'forgiven'.

This is a legal concept and relies on legal works of self-justification.

It is not of faith.

(Therefore it is sin.)

To think that one can exonerate oneself of each single sin by applying the correct amount of remorse, or penitence, at the correct time (desperately, before one dies) and the proper mode of confession in order to justify oneself . . . . is nothing to do with the gospel of Jesus Christ, wherein, Romans 1:17, is revealed (not the rightness of men but) the righteousness of God.

And that righteousness - of God - is revealed out of faith (it is ek) and unto faith (it is eis). Out of the faith of Jesus Christ ; and unto the faith of the believer.

God's righteousness (not man's superstition) is satisfied because it was demonstrated (see the special word for righteousness used in Romans 5:18 dikaioma, a demonstrated righteousness) upon his own Son.

By one (demonstrated) righteousness unto all humanity (under His headship) unto justification of life. [Literal Translation, see EGNT, with my brackets.]

The result of that demonstration of Divine righteousness was sufferings (he bore our sins in his own body on the tree, 1 Peter 2:24) and death (Christ died for our sins according to the scriptures, 1 Corinthians 15:3) and bloodshed (my blood ... which is shed for many for the remission of sins, Matthew 26:28).

That is how sins are remitted.

Not by the penitent's remorse, or fear, or terror as he feels his heart miss a beat and hurriedly tries to think whether or not he has confessed to every covetous thought, every lustful look, every envious sensation.

He that is entered into the rest (by faith) of God - has ceased from his own works, Hebrews 4:10.

Justification is by faith, not legal works.

And the gospel preaches that men are to give up all self-righteousness, of every kind (most of all the religious kind) and to depend utterly on God himself, through Jesus Christ.

With the heart man believeth . . . unto righteousness, Romans 10:10.

Righteousness, is of God alone. Humanity believeth.

And when that redemption (wrought out between the Father and the Son, through the eternal Spirit, Hebrews 9:14) is preached (by those sent of God to do so, who have experienced, themselves, the power of the gospel unto salvation, Romans 1:16) then the soul who believes, is advertised of the fact that all his sins have already been borne by Jesus Christ, the Son of God, 1 Thessalonians 1:10.

He is already delivered from wrath.

This, indeed, is a joyous sound. This, indeed, releases from legal terror and abject bondage. This is the silver sound of jubilee.

And, therefore, in believing that gospel, he is justified from all things whatsoever he hath done, Acts 13:39.

Thereafter he walks not by legal works, not by sight - but by faith, 2 Corinthians 5:7.

And there is no condemnation, Romans 8:1, to them which are in Christ Jesus who walk not after the flesh (in either worldliness or legal religion) but after the Spirit.

As to the steps of a son walking through this world, who is conscious of the eye of a father, 'My son, give me thine heart, and let thine eyes observe my ways (not legal ways),' Proverbs 23:26.

A father may chasten, a father may scourge, Hebrews 12:6, but it is not to condemnation, for the wrath is already past.

Be ye therefore perfect, even as your Father in heaven is perfect, Matthew 5:48. But no legal effort will achieve this. For whatsoever is not of faith - is sin. And the law is not of faith, Galatians 3:12.

This is the gospel.

What the question postulates, is something other than the gospel I find in my bible.

(Which is, I suppose, the reason that not one, single text of scripture is referred to by the question.)

I have answered this question as a lifelong Protestant, born into a household of four generations of Church of Scotland Ministers ; baptised, cognisantly and voluntarily, at the age of five, into that Protestant denomination ; then baptised as an adult at sixteen into the Baptist Assembly, another Protestant denomination ; then resident within Independent Protestant congregations for twenty five years ; and am now Director of Belmont Publications which publishes Protestant literature.