Summary

Here is a summary of this article, which examines whether a Christian can lose their salvation or not.

It's possible for righteous people (these are the saved) to stop being righteous, and so come under the Lord's judgement.

But when a righteous person turns away from his righteousness and does injustice and does the same abominations that the wicked person does, shall he live? None of the righteous deeds that he has done shall be remembered; for the treachery of which he is guilty and the sin he has committed, for them he shall die. Ezekiel 18:24 (ESV)

Paul knew this was possible, and guarded against it.

Do you not know that in a race all the runners compete, but only one receives the prize? So run that you may obtain it. Every athlete exercises self-control in all things. They do it to receive a perishable wreath, but we an imperishable. So I do not run aimlessly; I do not box as one beating the air. But I discipline my body and keep it under control, lest after preaching to others I myself should be disqualified. 1 Corinthians 9:24-27 (ESV)

We have to remain in Jesus in an ongoing way to keep our salvation.

But now he has reconciled you by Christ's physical body through death to present you holy in his sight, without blemish and free from accusation— if you continue in your faith, established and firm, not moved from the hope held out in the gospel. Colossians 1:22-23a (NIV)

It's not just up to us though. In fact, it's God who keeps us safe, and He enables us to continue in Him.

The LORD preserveth all them that love him: but all the wicked will he destroy. Psalm 145:20 (KJV)

If we fall away from God we must repent, and if we do God will take us back.

"Cast away from you all your transgressions which you have committed and make yourselves a new heart and a new spirit! For why will you die, O house of Israel?
"For I have no pleasure in the death of anyone who dies," declares the Lord GOD. "Therefore, repent and live." Ezekiel 18:31-32 (NASB^®)

The Bible offers strong evidence that just one unrepentant instance of some sins like adultery or murder leads to spiritual death. David's sin was an apparent example of this, until he confessed it.

Then David said to Nathan, “I have sinned against the LORD.”
Nathan replied, “The LORD has taken away your sin. You are not going to die. 2 Samuel 12:13 (NIV)

This suggests that even God's children should be deathly afraid of some sins.

Do you not know that the wicked will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor male prostitutes nor homosexual offenders nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God. 1 Corinthians 6:9-10 (NIV)

This doesn't mean we have to be literally perfect. Paul, a saved person, said he still had a sin nature.

For I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out. Romans 7:18 (ESV)

However, Paul controlled this sin nature (e.g. 1 Corinthians 9:24-27 above), relied on God to save him from it, and didn't indulge in sins like the people described in 1 Corinthians 6:9-10 above. He lived by the Spirit.

Therefore, brothers, we have an obligation—but it is not to the sinful nature, to live according to it. For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live, because those who are led by the Spirit of God are sons of God. Romans 8:12-14 (NIV)

There is clear teaching in the Bible that saved people can lose their salvation. It's not correct to think that every fallen Christian was never saved to begin with.

For if, after they have escaped the defilements of the world through the knowledge of our Lord and Savior Jesus Christ, they are again entangled in them and overcome, the last state has become worse for them than the first. For it would have been better for them never to have known the way of righteousness than after knowing it to turn back from the holy commandment delivered to them. 2 Peter 2:20-21 (ESV)

Jesus apparently taught that saved people can fall away.

Those on the rock are the ones who receive the word with joy when they hear it, but they have no root. They believe for a while, but in the time of testing they fall away. Luke 8:13 (NIV)

A major reason why this issue is so important to believe correctly about is that the Bible warns very strongly against false teachings.

But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction. And many will follow their sensuality, and because of them the way of truth will be blasphemed. And in their greed they will exploit you with false words. Their condemnation from long ago is not idle, and their destruction is not asleep. 2 Peter 2:1-3 (ESV)

To read about these things in more detail, continue on through the article.