In your answer you said, “According to the Bible both these fears are irrational. The only qualification we have to meet for the rapture is to be born again.” What Scripture references are you basing this upon? The only verse I can think of that perhaps clearly alludes to this question is Luke 21:36 “Watch therefore and pray always that you may be counted worthy to escape all these things that will come to pass…” – and this seems to be definitely at variance with your view.
Then you said, “After all what rational person, upon being given the chance to go straight to Heaven and be blessed for all eternity would say, “Someday Lord, but not today.” It doesn’t make sense.” I think a self-centered rational person who felt they had nothing further to do here would say yes. But a rational person who cared for the fate of the lost or loved ones during the Tribulation could legitimately wish for more time if they felt their mission wasn’t complete yet.
There being no indications of a partial rapture in the Bible, it stands to reason that all who are born again will be raptured. Several competent translations contain the word “about” in Luke 21:36. Young’s Literal Translation reads, “watch ye, then, in every season, praying that ye may be accounted worthy to escape all these things that are about to come to pass, and to stand before the Son of Man.” This places the warning in the context of the destruction of Jerusalem in 70 AD, about which the Lord had been speaking. There are no verses in Scripture indicating that the rapture is only for the worthy. If there were, none of us would be taken.
One of the most self-centered positions to hold is that the work of the Kingdom depends upon us. Job 38:5-8 says, “Look up at the heavens and see; gaze at the clouds so high above you. If you sin, how does that affect him? If your sins are many, what does that do to him? If you are righteous, what do you give to him, or what does he receive from your hand? Your wickedness affects only a man like yourself, and your righteousness only the sons of men.”
Jesus said, Upon this rock I will build my Church (Matt. 16:18) We have the privilege of helping, but our help is not required for the Kingdom to advance.
And Paul said, “How do you know, wife, whether you will save your husband? Or, how do you know, husband, whether you will save your wife?” (1 Cor. 7:16) He was speaking of the futility of thinking that given enough time we could soften the heart of another person. That’s the Holy Spirit’s job. True, we can preach and pray, but only the Holy Spirit can convict.