It is the position of Reformed theology, as well as some Arminian denominations, that one who has been given a true, saving faith by God cannot be lost.

Here are a few essays:
Can a Christian Lose His or Her Salvation? by Greg Johnson
Assurance of Salvation: Can I Really Be Sure? John G. Reisinger
The Blessing of Full Assurance May 13th, 1888 by C. H. SPURGEON

On one of my "favorite Christian women" bloggers, Carrie "Of Christian Women", started a series based on one of John MacArthur's sermon series. She was challenged with a series of "difficult" passsages.

I'm going through them here because it made for a rather long post.

"Therefore let anyone who thinks that he stands take heed lest he fall." 1 Cor 10:12

If you read the verse presupposing that "fall" means to lose one's salvation, then that is what you presuppose.

If you read the plain reading of the verse with an open mind, in context; if you look at the original language; if you look at other places in the New Testament were the same Greek word is used, you might come away with a different feeling.

This word "fall" is translated from the Greek (transliterated) "pipto" {pip'-to}.

The word has a few meanings. Looking at the rest of the verses that use the word "pipto" (it's used 93 times), it's fairly easy to see that it most often simply means "fall". To fall down. In this context: sin. Not lose one's salvation. We all sin - in fact, the Bible tells us (in 1 John 1:8) that if "we say we have no we deceive ourselves, and the truth is not in us."

Here's a couple of verses where "pipto" is used.

Matthew 13:4
And as he sowed, some seeds fell (pipto) along the path, and the birds came and devoured them.

Luke 8:41
And there came a man named Jairus, who was a ruler of the synagogue. And falling (pipto) at Jesus' feet, he implored him to come to his house,

Luke 6:39
He also told them a parable: "Can a blind man lead a blind man? Will they not both fall (pipto) into a pit?

There is no reason to believe this passage refers to losing one's salvation.

"For if God did not spare the natural branches, neither will he spare you. Note then the kindness and the severity of God: severity toward those who have fallen, but God's kindness to you, provided you continue in his kindness; otherwise you too will be cut off." Romans 11:21-22

Who is Paul talking to? What is the context?

Context would appear to tell us that Paul is talking about Israel and Gentiles.

If we allow Scripture to interpret Scripture (the many verses where it says that God gets to choose/elect), then we must look at a larger picture than just these few verses.

I'm going to quote a page by Sam Storms:

Does this passage imply that genuine believers can lose their salvation? Three things may be said.

(1) It may be that Paul is echoing a theme found elsewhere in his letters and throughout the NT, namely, that ultimate salvation is dependent on perseverance in faith (cf. Rom. 8:13; Col. 1:23; Heb. 3:6,14; 1 Peter 1:5; 1 John 2:19), a faith which God graciously preserves and sustains within us.

(2) Others have suggested that Paul's discussion here is about Gentiles as a class, considered collectively, and Israel as a class, considered collectively. In other words, just as "Israel" was cut off, so also "Gentiles" may be if they do not believe. [Speaking for myself, I don't find view (2) persuasive.]

(3) Moo has another explanation: "While the olive tree represents the true, spiritual people of God, those who are said to belong to this tree are not only those who, through their faith, are actually part of the tree but also those who only appear to belong to that tree. This is evident from the fact that Paul speaks of unbelieving Jews as having been 'cut off' from the tree (v. 17). In reality, these Jews had never been part of the tree at all; yet to preserve the metaphor he is using, Paul presents them as if they had been. In the same way, then, those Gentiles within the church at Rome – and elsewhere – who appear to be part of God's people, yet do not continue in faith, may never have been part of that tree at all" (707).

Views (1) and (3) may then be combined: Those who have truly believed will continue in God's kindness (Heb. 3:6,14). Those who do not continue in God's kindness show thereby that they were never truly part of the tree (on this, see esp. 1 John 2:19). Failure to persevere does not mean that one who was truly saved becomes truly lost. Rather, perseverance is itself the proof that one was truly saved. If one does not persevere, one has always been lost and never saved.

"And the ones on the rock are those who, when they hear the word, receive it with joy; but these have no root, they believe for a while and in time of temptation fall away." Luke 8:13

This verse needs to be answered with a question:

If a heart is "stony" (the soil these seeds fell on), is it a heart truly willing to follow and believe? Is a stony heart a heart with saving faith?

"For it is impossible to restore again to repentance those who have once been enlightened, who have tasted the heavenly gift, and have become partakers of the Holy Spirit, and have tasted the goodness of the word of God and the powers of the age to come, if they then commit apostasy..." (Hebrews 6:4)

Again, taken in context...if we go on to verse 9: "Though we speak in this way, yet in your case, beloved, we feel sure of better things--things that belong to salvation."

Quoting J.W.Hendryx:

If the author of Hebrews is confident of better things of the persons he is speaking with, things that belong to salvation, then obviously falling away does not belong to it. This is a clear statement that the author was not describing saving faith of those who are in danger of falling away in the preceding passage, because the kind of response that falls away, he says, are not among the "things that belong to salvation." So whatever the things the author just described about falling away in Heb 6:4-8 are not the characteristics of true regenerate persons. People can be enlightened and taste and partake .... They may be externally a part of the church and receive external blessings, yet if they abandon trust in Christ for ritual or something else, there is no hope for their salvation. They were never regenerate to begin with for falling away does not accompany or belong to true salvation, according to the text.

"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. Well, I do not run aimlessly, I do not box as one beating the air; but I pommel my body and subdue it, lest after preaching to others I myself should be disqualified." 1 Cor 9:24-27

Again, by Sam Storms:

More likely, however, is Paul’s concern that he not become slack or indifferent in his ministry lest he forfeit God’s approval on his apostolic endeavors (and perhaps the power of the Holy Spirit that energized his work). He fears not hearing God say: “Well done, good and faithful servant,” and thereby forfeiting the divine blessings and rewards he otherwise would receive (a theme he earlier addressed in 1 Cor. 3:10-15). The Greek word adokimos (translated “disqualified”) does not pertain to the test of faith but to the test of apostleship. In 2 Corinthians Paul applies the terminology of testing (adokimos and its cognates) to himself as an apostle, not as a professing Christian (see 13:6-7; cf. 1 Thess. 2:4; 2 Tim. 2:15. Gundry-Volf concludes: “The fact that no instance of the use of adokimos or a cognate referring to Paul relates to the test of faith or salvation, rather, that every instance has to do with his fitness as an apostle raises doubts about the view that adokimos in 1 Cor. 9:27 means rejected from salvation and suggests instead that it means rejected as an apostle” (236-37).