I am absolutely confident no true believer in Jesus Christ will ever lose his or her salvation. Authentic believers can never do anything to forfeit the eternal life that is ours in Christ. Otherwise, by definition, it could not be said that we have everlasting life and will not come into judgment, but have passed from death to life (John 5:24).
"Blessed be the God and Father of our Lord Jesus Christ! According to his great mercy, he has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you, who by God's power are being guarded through faith for a salvation ready to be revealed in the last time" (1 Peter 1:3-5).
'm not fond of the expression "eternal security" because of the way the doctrine is abused by antinomians and people who think it's possible to own Jesus as Savior without bowing to Him as Lord. I prefer to speak of the perseverance of the saints, because that expression better captures the gist of what the doctrine entails.
The idea is not that if we once "accept Christ" we are guaranteed heaven regardless of whether we continue in the faith or not, but that those who are truly regenerate will not depart from Christ. The supposed Christian who does depart demonstrates that he was never a true Christian in the first place: "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 it might become plain that they all are not of us" (1 John 2:19).
On the other hand, I'm convinced that the saints will persevere not because I have any confidence in the saints' own strength or their own faithfulness. My own security not does not rest in my devotion to Christ, but in His devotion to me. I am "kept by the power of God." His power is what energizes my faith and keeps me in the process of salvation, ready to be revealed at the last time.
That's an echo of the truth of 2 Thessalonians 3:3: "The Lord is faithful. He will establish you and guard you against the evil one." And 2 Timothy 2:13: "If we are faithless, he remains faithful—for he cannot deny himself." Also, Jude 24: God "is able to keep you from stumbling and to present you blameless before the presence of his glory with great joy."
So on the authority of Scripture I believe absolutely in the doctrine of the perseverance of the saints. But it's not because I have any confidence in the saints themselves. It is God who secures their perseverance.