Someone in our church asked me for verses related to the notion that unbelievers will have a chance to repent after they die. She was sure that the notion was unbiblical, but where stands in written? I referred her to a helpful section of Wayne Grudem's Systematic Theology on this topic that pointed to several important scriptures on the topic. If you don't have this book you should get it and you can order it here.
Here is what Grudem writes:
Scripture never encourages us to think that people will have a second chance to trust in Christ after death. In fact, the situation is quite the contrary. Jesus' story about the rich man and Lazarus gives no hope that people can cross from hell to heaven after they have died: though the rich man in hell called out, "Father Abraham, have mercy upon me, and send Lazarus to dip the end of his finger in water and cool my tongue; for I am in anguish in this flame," Abraham replied to him, "Between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us" (Luke 16:24-26).The book of Hebrews connects death with the consequence of judgment in dose sequence: "just as it is appointed for men to die once, and after that comes judgment . . ." (Heb. 9:27). Moreover, Scripture never represents the final judgment as depending on anything done after we die, but only on what has happened in this life (Matt. 25:31-46; Rom. 2:5-10; cf. 2 Cor. 5:10).
...We should also realize that the idea that there will be a second chance to accept Christ after death is based on the assumption that everyone deserves a chance to accept Christ and that eternal punishment only comes to those who consciously decide to reject him. But certainly that idea is not supported by Scripture: we all are sinners by nature and choice, and no one actually deserves any of God's grace or deserves any opportunity to hear the gospel of Christ—those come only because of God's unmerited favor. Condemnation comes not only because of a willful rejection of Christ, but also because of the sins that we have committed and the rebellion against God that those sins represent (see John 3:18).
The idea that people have a second chance to accept Christ after death would also destroy most motivation for evangelism and missionary activity today, and is not consistent with the intense missionary zeal that was felt by the New Testament church as a whole, and that was especially exemplified in the missionary travels of the apostle Paul...
You can read the entire section here.