There are three main views when it comes to the question of whether or not a Christian can lose their salvation: "Yes, through sin", "yes through apostasy", and "no, never".
To answer "yes, through sin" is utter heresy. Salvation, as we all know, is offered by God's grace, and received by faith in His Son. It is explicitly stated as being a gift from God, received not by works, and that works actually cancel out grace. If salvation is by grace, it cannot be of works. If salvation is by works, it cannot be by grace. This can all be found in scriptures such as Ephesians 2:8-10, Romans 6:23, and especially Romans 11:6.
So, evidently, you cannot lose salvation by works. But there is one thing that could theoretically lose a man his salvation: Apostasy. Proponents of this particular view often cite Judas as their example. The simple question to ask here is, did God know that this person would apostatise? The correct answer, of course, is yes. God not only knows who will apostatise, and when, but in effect, He is even sovereign over this.
See, first, if God knows someone will apostatise in the future, He has no need to grant them salvation in the present. The apostate does not lose salvation because they never had salvation to lose! Furthermore, their apostasy both proves this, and was intended to prove this. In 1 John 2:19, we read "They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us."
So you see how apostasy is proof that a person was not saved. They "went out that they might be made manifest, that none of them were of us." Why is this? Well, "if they had been of us, they would have continued with us". This is because a true Christian, i.e. someone who is truly saved, is sealed by the Holy Spirit, guaranteeing eternal life (2 Corinthians 1:22; Ephesians 1:13, 4:30). He is more than capable of doing this (Jude 1:24), and we see that, actually, the fullness of the Godhead, i.e. the Father, Son, and Holy Spirit, are involved in this process (John 10:28-29).
Thus, the question of whether or not a Christian can lose their salvation has a very clear answer: no, they absolutely cannot. Salvation is by grace through faith, not of works, and so no work can either gain or maintain salvation by definition alone. Since the criteria for receiving salvation is faith, apostasy would result in the loss of salvation, however God's own omniscience means He foresees apostasy before it happens, causing Him to withhold salvation from the apostate. By contrast, He is sovereign, and mighty to save the believer, ensuring that once someone has been saved, they remain saved, as all three persons of the Godhead maintain our salvation eternally, and without condition. A true Christian can never apostatise, and so the one thing that could cause us to lose salvation can never occur. Conditional Security, therefore, ranges from misguided to heretical, but can never be considered sound doctrine.