***DISCLAIMER*** This is not an exhaustive post (see here for an explanation of the objective this post hopes to accomplish).
Before answering the question itself, it is important to define some terms within the question. It is necessary to define both “Christian” and “salvation.”
A Christian is someone who both confesses with his/her mouth that Jesus Christ alone is Lord and believes in his/her heart that God raised Him from the dead (Romans 10:8-17; Matthew 10:32; Luke 12:8; 1 Corinthians 12:3; Acts 16:31). Jesus Christ, the Son of the living God, is the only way by which mankind may be saved (Acts 4:12; John 14:6; Isaiah 43:11).
You might be asking, “Why would someone need to trust in Jesus Christ for salvation?” The reason for this is because all have sinned and fallen short of the glory of God (Romans 3:23). Every person has this sin problem. This problem began when Adam and Eve sinned in the Garden of Eden (Genesis 2-3). Because of this sin problem, we cannot save ourselves (Matthew 5:48; Isaiah 43:11, 64:6; Ephesians 2:1-3). God, a loving God as well as a just God who must punish sin (1 John 4:8; Exodus 34:7; Romans 2:8-10; 2 Thessalonians 1:6-10), solved this sin problem in the person of Jesus Christ. Jesus Christ, the infinite God-man, died on the cross and rose from the dead to pay the penalty for our sins and purchase a place in heaven for us (John 1:1, 14, 29; 1 Timothy 1:15; Isaiah 53:6). A Christian receives this free gift of eternal life via a trusting, saving faith in Jesus Christ alone (Acts 16:31; Romans 10:17; Galatians 3:2; Romans 6:23; 2 Timothy 2:24-26). It is neither done by works nor by head knowledge (Ephesians 2:8-9; James 2:19). It is by faith (Ephesians 2:8-9). As a result of this saving faith, the Christian walks in the good works Christ has called him/her to do, bearing fruit in keeping with repentance, among other things (Ephesians 2:10; Matthew 3:8; Titus 3:8).
One must understand that salvation, or heaven, is a free gift from God received by faith (Romans 6:23; Ephesians 2:8-9; Romans 10:17). As mentioned, it is not something earned by works or obtained by head knowledge (Ephesians 2:8-9; James 2:19). Instead, these works, which are good, are byproducts of salvation (Ephesians 1:4, 2:10, 4:1; Titus 2:14). Furthermore, better knowledge of who Jesus is (knowledge that should flow from the head to the heart) should also be a byproduct of this salvation.
With a good knowledge of what a Christian is and what salvation is, the question of whether or not a Christian can lose salvation can now be answered. No less than three passages help answer this. Before getting into them, one must understand that the entire Bible is living, active and inspired of God and profitable for many great things (2 Timothy 3:16-17; Hebrews 4:12; John 10:35). Furthermore, God says Himself that He does not lie, He does not change, and He is the same yesterday, today and forever (Numbers 23:19; Titus 1:2; Malachi 3:6; Hebrews 13:8). If God has inspired the entire Bible and He says Himself that He cannot lie, then that would make the entire Bible true. As a result, we can trust the following passages that address whether or not a Christian can lose his/her salvation (in addition to the passages already mentioned in this article).
In John 10:22-30 (NASB), we read the following:
22 At that time the Feast of the Dedication took place at Jerusalem; 23 it was winter, and Jesus was walking in the temple in the portico of Solomon. 24 The Jews then gathered around Him, and were saying to Him, “How long will You keep us in suspense? If You are the Christ, tell us plainly.” 25 Jesus answered them, “I told you, and you do not believe; the works that I do in My Father’s name, these testify of Me. 26 But you do not believe because you are not of My sheep. 27 My sheep hear My voice, and I know them, and they follow Me; 28 and I give eternal life to them, and they will never perish; and no one will snatch them out of My hand.29 My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of the Father’s hand. 30 I and the Father are one.”
In asserting His deity, Jesus Christ plainly states that His sheep know His voice and follow Him (verse 27). He gives eternal life to them (verse 28). Furthermore, He says twice that nobody can snatch them out of His Father’s hand (verse 29; see also John 6:37, 44; 17:6, 9, 12, 15, 19; 18:9). He goes on to say that He and the Father (which is God) are one (verse 30). As mentioned, the entire Bible is true and without error. As a result, when Jesus Christ says that His sheep both have eternal life and cannot be snatched out of his hand, He means exactly that. This supports the fact a Christian cannot lose his/her salvation.
Romans 8:1-39 is another passage showing how a Christian cannot lose salvation. The apostle Paul states how no condemnation exists for those in Christ Jesus (verse 1). Paul goes on to explain how the law of the Spirit of life (the Holy Spirit, specifically) sets one free from the law of sin and death (verses 2-4; see also John 8:36). The person who has the Spirit of Jesus dwelling in him/her is given life to his/her mortal body (verse 11). Furthermore, God adopts those led by the Spirit (verses 14-23). Verses 28-39 (NASB) also give excellent insight:
28 And we know that God causes all things to work together for good to those who love God, to those who are called according to His purpose. 29 For those whom He foreknew, He also predestined to become conformed to the image of His Son, so that He would be the firstborn among many brethren; 30 and these whom He predestined, He also called; and these whom He called, He also justified; and these whom He justified, He also glorified. 31 What then shall we say to these things? If God is for us, who is against us?32 He who did not spare His own Son, but delivered Him over for us all, how will He not also with Him freely give us all things? 33 Who will bring a charge against God’s elect? God is the one who justifies; 34 who is the one who condemns? Christ Jesus is He who died, yes, rather who was [l]raised, who is at the right hand of God, who also intercedes for us. 35 Who will separate us from the love of Christ? Will tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? 36 Just as it is written,
“For Your sake we are being put to death all day long;
We were considered as sheep to be slaughtered.”
37 But in all these things we overwhelmingly conquer through Him who loved us.38 For I am convinced that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, 39 nor height, nor depth, nor any other created thing, will be able to separate us from the love of God, which is in Christ Jesus our Lord.
Those who have been justified by Christ can never be separated from Christ’s love by anything. He is our justifier, our advocate and our Savior (verses 30-39; see also Romans 3:28; 5:1, 9; Galatians 2-3; 1 John 2:1).
Finally, Ephesians 4:30 states, “Do not grieve the Holy Spirit of God, by whom you were sealed for the day of redemption.” To be sealed is to be sealed for security from Satan. Ephesians 1:13-14 states, “In Him, you also, after listening to the message of truth, the gospel of your salvation – having also believed, you were sealed in Him with the Holy Spirit of promise, who is given as a pledge of our inheritance, with a view to the redemption of God’s own possession, to the praise of His glory” (see also 2 Corinthians 1:21-22). As mentioned earlier, Satan cannot pluck a believer from Jesus’ hand. Clearly, we see this throughout the Scriptures. Therefore, it is not possible for a Christian to lose his/her salvation.