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I take it that the perseverance of the saints relates first and foremost to continual faith in the Lord. Second, it relates to growth in grace. Now, that growth can have ups and downs, just like the stock market. And there are times when believers do things that do not honor the Lord sufficiently for him to remove them from life on earth. But even when believers sin, they are growing in grace. You will note that Paul says that many believers have fallen asleep (1 Cor 11.30) because they did not observe the Lord's Supper properly. But he adds, "But if we examined ourselves, we would not be judged. But when we are judged by the Lord, we are disciplined so that we may not be condemned with the world" (1 Cor 11.31-32). The death of the people in v. 30 is clearly the death of Christians, since the word Paul uses is "sleep." This is used almost entirely consistently in the Bible, when referring of death, to refer to the death of a believer (because death does not have the final say). But this death is essentially discipline. The Bible is filled with examples of believers undergoing all sorts of discipline from the Lord, yet they are still believers. And even when we are undergoing discipline in one area, it doesn't mean that the whole of our life is in need of discipline. If you are a parent, you know what I'm talking about. If a child needs to be disciplined, this doesn't mean that everything in his or her life is wrong. But there has been an infraction and it needs to be dealt with.
This is the only way I know how to harmonize those passages that speak of our perseverance and those that speak of us being disciplined, even to the point of death. The temptation that many of us have is to ignore one set of verses and insist only on the other. But, like many things in scripture, I take it that this is a tension, a mystery, that we need to wrestle with as well as we can. But in the end, we need to trust the Lord.