No. Salvation is the work of God: secured by Christ, sealed by the Spirit, and kept by His power. Those who truly belong to Him cannot be snatched from His hand. Scripture's warnings against falling away call us to persevere in real faith, not to doubt God's ability to keep His own.
Not a summary of these passages: the passages themselves. Read them, then come back to the study below.
The study
What the Scripture says
1
The Shepherd holds His sheep
Jesus said His sheep hear His voice, He knows them, they follow Him, and He gives them eternal life: 'They will never perish, and no one will snatch them out of my hand.' The Father who gave them is greater than all, and no one can snatch them out of the Father's hand either.
My sheep hear my voice, and I know them, and they follow me. I give eternal life to them. 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. No one is able to snatch them out of my Father’s hand.
Paul lists the worst that could be named: tribulation, distress, persecution, famine, nakedness, peril, sword, even death itself, and asks: 'Who shall separate us from the love of Christ?' His answer is a trumpet: neither death nor life, nor anything in all creation, can separate us from the love of God in Christ Jesus our Lord.
Who shall separate us from the love of Christ? Could oppression, or anguish, or persecution, or famine, or nakedness, or peril, or sword? Even as it is written, “For your sake we are killed all day long. We were accounted as sheep for the slaughter.” No, in all these things, we are more than conquerors through him who loved us. For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor any other created thing, will be able to separate us from the love of God, which is in Christ Jesus our Lord.
'He who began a good work in you will complete it until the day of Jesus Christ.' Jesus said of those the Father gives Him: 'I should lose nothing, but should raise him up at the last day,' and 'He who comes to me I will in no way throw out.' Your keeping rests on His faithfulness, not your grip.
being confident of this very thing, that he who began a good work in you will complete it until the day of Jesus Christ.
All those whom the Father gives me will come to me. He who comes to me I will in no way throw out. For I have come down from heaven, not to do my own will, but the will of him who sent me. This is the will of my Father who sent me, that of all he has given to me I should lose nothing, but should raise him up at the last day.
Scripture warns solemnly against falling away (Hebrews 6:4-6), and those warnings are meant to keep us clinging to Christ; genuine faith perseveres. John explains that those who left 'didn't belong to us; for if they had belonged to us, they would have continued with us.' Real children keep abiding.
For concerning those who were once enlightened and tasted of the heavenly gift, and were made partakers of the Holy Spirit, and tasted the good word of God, and the powers of the age to come, and then fell away, it is impossible to renew them again to repentance; seeing they crucify the Son of God for themselves again, and put him to open shame.
They went out from us, but they didn’t belong to us; for if they had belonged to us, they would have continued with us. But they left, that they might be revealed that none of them belong to us.
Remain in me, and I in you. As the branch can’t bear fruit by itself, unless it remains in the vine, so neither can you, unless you remain in me. I am the vine. You are the branches. He who remains in me, and I in him, the same bears much fruit, for apart from me you can do nothing.
John wrote his first letter 'that you may know that you have eternal life': certainty, not guesswork. The Holy Spirit witnesses with our spirit that we are God's children. The question is not 'Am I good enough to keep it?' but 'Have I truly trusted the One who is strong enough to keep me?'
The testimony is this, that God gave to us eternal life, and this life is in his Son. He who has the Son has the life. He who doesn’t have God’s Son doesn’t have the life. 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, and that you may continue to believe in the name of the Son of God.
For you didn’t receive the spirit of bondage again to fear, but you received the Spirit of adoption, by whom we cry, “Abba! Father!” The Spirit himself testifies with our spirit that we are children of God;
They went out from us, but they didn’t belong to us; for if they had belonged to us, they would have continued with us. But they left, that they might be revealed that none of them belong to us.
My sheep hear my voice, and I know them, and they follow me. I give eternal life to them. 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. No one is able to snatch them out of my Father’s hand.
For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor any other created thing, will be able to separate us from the love of God, which is in Christ Jesus our Lord.
All those whom the Father gives me will come to me. He who comes to me I will in no way throw out. For I have come down from heaven, not to do my own will, but the will of him who sent me. This is the will of my Father who sent me, that of all he has given to me I should lose nothing, but should raise him up at the last day.