Despite numerous statements to the contrary, there are many denominations, churches and individuals who believe salvation is possible to lose. The two prevailing views are conditional security, and eternal security, also informally known as "once saved always saved".
Conditional security is easy to refute simply because it is a works-based gospel. The Bible repeatedly affirms that salvation is by grace, through faith, and not of works, even to the point of telling us that if we attempt to be justified by works, we have "fallen from grace" (Galatians 5:4). But in John 10:27-29, we find a second argument against conditional security: God's sovereignty.
Every statement about salvation in the Bible is objective and present. "These things I have written to you who believe in the name of the Son of God, that you may know that you have eternal life..." (1 John 5:13). "if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved." (Romans 10:9). "help these women who labored with me in the gospel, with Clement also, and the rest of my fellow workers, whose names are in the Book of Life." (Philippians 4:3). Salvation is never seen as something that those who possess it can ever lose. John 10:27-29 is no exception. In it, Jesus tells us that His "sheep" shall never perish, and further qualifies that statement with "neither shall anyone snatch them out of my hand". Then He backs up this statement by reminding us just how powerful God is. No one is greater than God, so because Jesus' sheep have been given to Him by God, it is impossible for any living being, be it man, beast or demon, to take them from Him.
That includes the sheep themselves. If no one can take you from Jesus' hands, and you are someone, then you cannot take you from Jesus' hands. As an arrogant species, we tend to think salvation is all about us. And of course, salvation is, at least partially, about us, simply because we are the ones being saved. But just as everything else in this universe is really about God, so also is our salvation about God. He does it for us, but also for His own purpose (2 Timothy 1:9, which also happens to tell us our salvation is not based on our works). So, conditional security is just plain arrogant, and borderline blasphemous (I say borderline because although it has blasphemous implications, the individual believer rarely has blasphemous motives). My Christian brethren, I say this with huge amounts of joy in my heart: You are not powerful enough to lose your salvation.