Thoughts... 2 Cor. 10:5 tearing down misleading arguments and every high place [fig., arrogance] lifting itself up against the knowledge of God, and bringing every thought into captivity to the obedience of Christ.
It appears from the title of this thread that you take this verse as a threat. I conclude that you read such into the text as you comment,"there is the strong possibility they could have their names blotted out of the book of life." And to make matters worse you then add your own twist on the verse with your words,"If they didn't overcome what? Maybe habitual sexual sin for starters or some other form of idolatry?"
Rather than being a threat as you make it out to be,it is a promise to the afflicted and persecuted believers which John writes to,to encourage them to endure in their faith in their time of great temptation.
You and others who use this verse as you do,stretching its implications to support the false doctrine of Christ losing one of His sheep for whom He died, is insideous,as it is an insult to Christ(also to the Father and Sprit as they're One),and harmful to weak believers(those weak in faith or those struggling with temptation and sin).
The promise as expressed in the greek states, "I will not" —Greek, "I will not by any means." The "I will not" is followed by the affirming "I will". He first says to them what He won't do,and He next says what He will do. Praise be to God. All Glory to Him and His Faithfulness to us.
Rev 3:5 '"The one who is conquering, he shall be clothed in white garments, and under no circumstances will I be erasing his name from the scroll of life, and I will be avowing his name in front of My Father and before His messengers."
Rev 3:5 'The one overcoming, this [one] will be clothed in white garments, and by no means will I blot out his name from the Scroll of Life, and I will confess his name before My Father and before His angels.
Rev 3:5 The one who conquers will be clothed thus in white garments, and I will never blot his name out of the book of life. I will confess his name before my Father and before his angels.
1 John 5:4 because every one who is begotten of God doth overcome the world, and this is the victory that did overcome the world--our faith;
1 John 5:4 For every child of God overcomes the world; and the victorious principle which has overcome the world is our faith.
1 John 5:4 Because, whoever is born of God, overcometh the world: and this is the victory that overcometh the world, our faith.
1 John 5:4 Because every one having been begotten from God overcomes the world, and this is the victory having overcome the world — your faith!
this is the victory that overcometh — Greek aorist, “... that hath (already) overcome the world”: the victory (where faith is) hereby is implied as having been already obtained (1Jo_2:13; 1Jo_4:4). JFB
One commentators comments on Rev. 3:5 are as follows:
Christ promises every true Christian that He will not erase his name from the book of life, but will confess his name before the Father and before His angels. Incredibly, although the text says just the opposite, some people assume that this verse teaches that a Christian's name can be erased from the book of life. They thus foolishly turn a promise into a threat. Exodus 32:33, it is argued by some, supports the idea that God may remove someone's name from the Book of Life. In that passage the Lord tells Moses that "whoever has sinned against Me, I will blot him out of My book." There is no contradiction, however, between that passage and Christ's promise in Revelation 3:5. The book referred to in Exodus 32:33 is not the Book of Life described here, in Philippians 4:3, and later in Revelation (13:8; 17:8; 20:12, 15; 21:27). Instead, it refers to the book of the living, the record of those who are alive (cf. Ps. 69:28). The threat, then, is not eternal damnation, but physical death.
In John's day, rulers kept a register of the citizens of a city. If someone died, or committed a serious crime, their name was erased from that register. Christ, the King of heaven, promises never to erase a true Christian's name from the roll of those whose names were "written from the foundation of the world in the book of life of the Lamb who has been slain" (13:8).
On the contrary, Christ will confess every believer's name before God the Father and before His angels. He will affirm that they belong to Him. Here Christ reaffirmed the promise He made during His earthly ministry: "Everyone who confesses Me before men, I will also confess him before My Father who is in heaven" (Matt. 10:32). The comforting truth that true Christians' salvation is eternally secure is the unmistakable teaching of Scripture. Nowhere is that truth more strongly stated than in Romans 8:28--39 - John MacArthur.