Students of the Bible vary on the answer to this question, but as I understand the Scripture, the answer is yes. If a person truly trusted in Christ, then he cannot lose his salvation. He will lose rewards and experience serious consequences in this life, sometimes even the sin unto physical death, but since our salvation is based on the finished work of Christ, we are kept by the power of God and His sovereign work. Several passages stress this.
Romans 8:32-39 He who did not spare His own Son, but delivered Him up 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 raised, who is at the right hand of God, who also intercedes for us. 35 Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? 36 Just as it is written, “For Thy 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, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
The emphasis here is that nothing—no condition or person, and this would include the person himself—can separate the believer from God. The conditions listed include height and depth which would certain have application to the depths of falling away even in unbelief.
We need to recognize that when someone abandons their faith, this is really the result of a process of sin. If we could lose our salvation, then in the final analysis, we would be saved by not sinning or by works.
Another passage that bears on this is 2 Tim. 2:10-13.
10 For this reason I endure all things for the sake of those who are chosen, that they also may obtain the salvation which is in Christ Jesus and with it eternal glory. 11 It is a trustworthy statement: For if we died with Him, we shall also live with Him; 12 If we endure, we shall also reign with Him; If we deny Him, He also will deny us; 13 If we are faithless, He remains faithful; for He cannot deny Himself.
This is written concerning “those who are chosen, that they may obtain the salvation…” The “chosen” or “elect” always refers to those who are already saved as is clear here. Since all believers, through their position and co-identification with Christ share in his life and death (Rom. 6), they have died with Him and will live with Him. If they endure in this life they will be rewarded and this, includes the promises of reigning with Him as also promised in Rev. 2-3 to the seven churches.
On the other hand, if we deny Him in some way, the point is that He will deny us, not salvation, but as the preceding context shows, He will deny us rewards (see 1 Cor. 3:12ff). Our faithfulness does not change His faithfulness. He remains faithful for He cannot deny Himself. In His faithfulness, He has promised us eternal life through our union in Him and His finished work. To deny us salvation would be to deny Himself for we are in Him, joined into union with His life (again compare Romans 6).
For more on this issue let me encourage you to check out the Grace Evangelical Society web site at http://www.faithalone.org.