What would be an orthodoxly Christian, biblically based response to a concern that a Christian could die without repenting of a given sin?

Query 1) What is the fate of those who believe in Jesus Christ but who die without repenting of something they never discovered was sinful (Simon, Acts 8, given as an example.)

This example is of one who believed and was baptised. Although at the time of his request to buy power he didn't think that was a sin (given his track-record before becoming a Christian, we can see where he was coming from), the apostles outrightly condemned that sin so that Simon was in no doubt that only his repentance, and prayer for forgiveness, would deal with this sin. But the Bible account does not tell us any more. And why should it? What is stated stands for all time, for all believers. We might like to know more, but what has been revealed is sufficient for us. The account of this new convert, Simon, shows they have much to learn, and they need to be diligent in identifying sin and shunning it.

However, this example does not fit the bill of query 1. Simon DID discover his sin and the imperative of repenting of it without delay.

Query 2. "Apparently, Simon stood 'poisoned by bitterness and bound by iniquity' before repenting and praying for forgiveness despite not knowing [his] sinfulness."

Well, it's the other way around. He did not know his desire was sinful until the apostle rebuked him and told him that he was poisoned by bitterness and bound by iniquity. Then came the realisation that urgent repentance and prayer was called for. Conviction of sin is the work of the Holy Spirit (John 16:8), and here is a case where a new convert was convicted due to Holy Spirit revelation to the apostles of what, exactly, was the problem with Simon.

Query 3. "Does a person stand unsaved if they fail to learn of and pray for even one type of sin they've committed?"

The only people who will stand, and remain, unsaved, are those who never come to saving faith in Christ. They are detailed in the Bible as "them that perish because they received not the love of the truth, that they might be saved... all might be damned who believe not the truth but had pleasure in unrighteousness." (2 Thessalonians 2:10-12)

It matters not how many sins they have committed, or whether they know those to be sins or are unaware of the unconfessed sin in their life. The gospel of Christ is the good news of truth, life, forgiveness, love and acceptance in the Beloved. All who enter into that blessed relationship with God, through faith in Christ, trust utterly on Christ's finished work on the cross to deal with all their sin. And, once he has liberated them from slavery to sin, he is their master whom they love to obey. This new relationship is based on the grace of God, not the ability of individuals to maintain a perfect standard, for that's an impossibility. Here is how this doctrine (detailed in Colossians 2:2-14) is explained in this book:

"That is the doctrine. When Christ rose, all his elect rose in him. In process of time they are called. That is, called by the voice of the Son of God into this very same gospel. The voice of the Son speaks within of having already obtained eternal redemption for his people; of his having now achieved everlasting reconciliation on their behalf; of unconditional salvation having been effectually outwrought by the blood of his cross in their stead.

And as, within, Christ testifies of all that he had before accomplished in death, the Spirit bears witness with the doctrine taught in the gospel of the grace of Christ, the gospel of God concerning his Son [Romans chapter 8]. Faith, the gift of God within the saints, credits the truth of this gospel in its entirety. Faith stands to the doctrine. Now comes the exhortation: 'If ye then be risen with Christ, seek those things which are above, where Christ sitteth on the right hand of God.'

Christ has taken the saints through death, and up into life from the other side of death. That is the doctrine. Their experience, whom he calls, answers to this: having believed, they have life in his name.

That life is eternal: it is everlasting life. It flows from the resurrection and ascension of the Son of God. ...Everlasting life beyond the reach of death fills the saints and testifies to the truth of the doctrine of Christ: they rose when he rose. 'If ye then be risen with Christ' - then - 'set your affections on things above, not on things on the earth'. 3.2

...Carnality with its corruptions is still active. But faith appropriates the place Christ took at the cross on one's behalf, and reckons all dead, despite the clamour of the flesh for the attention of the soul. ...Neither the flesh nor the things of the earth are dead to us; no, but we are dead to it and to them, and, already, within, are risen in newness of life. In this we dwell, and by this set our affections on the heavenly Son in the glory, his God our God, and his Father our Father.

Of course we are dead: we died when he died. This did not happen to us: it happened to him." Colossians, John Metcalfe, pp55-57

Conclusion: If Simon's new-found faith was, indeed, faith in the doctrine of Christ, he would be enabled to deal with any on-going sins of the flesh by the grace of God, because he would already have died (spiritually) and been raised (spiritually) with Christ. There would be no hope for anybody to avoid dying unsaved for lack of confessing even one sin they either knew of, or did not know of.

Christ delivers repentant sinners from their slavery to sin. He is then their master and he lovingly aids them to walk in his light till they are with him in glory. Having been totally forgiven after initial repentance, the faith they have in him ensures they rush to him for his aid when sin becomes a problem again. And he brings them through that. "Wherefore he is able to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them" (Hebrews 7:25). The only people who die unsaved are those who never have turned in repentance, putting all their trust in Christ's finished work on the cross. That work of pardon and salvation was perfect.

It was only to people who did not know him or his Father that he warned, "You will die in your sins" (John 8:21). Christians know the Son and the Father. They will not die in their sins.