In John 10, the Jews pressed Jesus to speak plainly if he was the Christ. Jesus answered, "I told you and you do not believe. The works that I do in my Father's name bear witness about me, but you do not believe because you are not among my sheep."
"My sheep hear my voice, and I know them, and they follow me. I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of my Father's hand. I and the Father are one."
It is God who gives us eternal life, and it is God who keeps us there. In Jude 24, we are told it is by the his power that we are kept from stumbling and presented blameless before him. In Ephesians 4:30, Paul writes that in Christ we are "sealed for the day of redemption." And in John 3:16, those who believe in Christ are given eternal life.
If it was possible to lose that gift of eternal life, then it wasn't eternal. If you could lose salvation, then you haven't been saved. It is by no work of our own that we are saved, and it is by no work of our own that we stay saved. It is from beginning to end the gracious work of God.
If a person confesses to being a follower of Jesus for a time, but then falls away, then they were never rooted in Christ to begin with, which Jesus explained in the parable of the sower.
But for those of us who have been called out of darkness and into his marvelous light, take heart, Christian. For nothing in all of creation will be able to separate us from the love of God that is in Christ Jesus our Lord when we understand the text.