Some of this concept comes because Mormons don't really want to acknowledge that many people will be eternally sent to hell. Its a harsh concept, there's no way around it, and many people want to find a way to keep their unbelieving loved ones out of hell. This is why Mormons and other universalists believe that God gives at least one more chance to people after death and that everyone can achieve salvation somehow.
The realities in the Bible are far different than this, though. Its hard to swallow, but if we can accept that Jesus was the perfect sacrifice for our sins, the vessel for God's wrath against us, only if we're faithful to him, then we also have to accept that those who do not accept him must become vessels of God's wrath.
Let me make this clear from the start. There is no where--no where--in the Bible that indicates a second chance after death. Death seals the deal. After death comes judgment. Any waiting period between the two is not a chance to learn and change one's mind. Either one accepted the one true God, or they didn't. Hebrews 11:6 tells us that one must have faith and believe in his existence when coming before God or they cannot please him. Since all will have faith in him when confronted with the reality of his being before us, this means that we have to have this faith before we have reality in front of us after death.
There is also no indication that hell lasts only X amount of time and then is finished. It is true, though, that people will be punished in hell according to their lives. Someone who lived a good life but never believed will be punished far less severely than someone who was the worst sort of criminal. None of it will ever bring them into the presence of God for eternity (heaven), however.
Here's some things taught about hell in the New Testament.
"When once the master of the house has risen and shut the door, and you begin to stand outside and to knock at the door, saying, 'Lord, open to us,' then he will answer you, 'I do not know where you come from... Depart from me, all you workers of evil!' In that place there will be weeping and gnashing of teeth, where you see Abraham and Isaac and Jacob and all the prophets in the kingdom of God but you yourselves cast out." Luke 13:25-28
"So it will be at the close of the age. The angels will come out and separate the evil from the righteous and throw them into the fiery furnace. In that place there will be weeping and gnashing of teeth." Matthew 13:49-50
"'Truly, I say to you, as you did not do it to one of the least of these, you did not do it to me.' And these will go away into everlasting punishment, but the righteous into everlasting life." Matthew 25:45-46
"God considers it just to repay with affliction those who afflict you, and to grant relief to you who are afflicted as well as to use, when the Lord Jesus is revealed from heaven with his mighty angels in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus. They will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might." 2 Thessalonians 1:6-9
"The dead, great and small, standing before the throne, and books were opened...and the dead were judged by what was written in the books, according to what they had done...and they were judged, each one of them, according to what they had done. Then Death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. And if anyone's name was not found written in the book of life, he was thrown into the lake of fire." Revelation 20:12-15
These, of course, are not the only references in the New Testament to hell and eternal punishment. Although it develops over time, we see hints of hell in the Old Testament as well. Hell is generally associated with fire or darkness, and is often referred to as everlasting or a similar term. It is very clear that those who do not believe in God and follow Christ will not be saved from hell.
Its not a pretty doctrine, but it does do one thing for us. It shows God's power, mercy, and love on the cross even more brightly and amazingly.