While there is no passage that specifically says, “Once saved, always saved,” there are passages like Romans 8:32-39 which in essence say this:
He who did not spare His own Son, but delivered Him up for us all, how will He not also with Him freely give us all things? 33 Who will bring a charge against God’s elect? God is the one who justifies; 34 who is the one who condemns? Christ Jesus is He who died, yes, rather who was raised, who is at the right hand of God, who also intercedes for us. 35 Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? 36 Just as it is written, “For Thy sake we are being put to death all day long; We were considered as sheep to be slaughtered.” 37 But in all these things we overwhelmingly conquer through Him who loved us. 38 For I am convinced that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, 39 nor height, nor depth, nor any other created thing, shall be able to separate us from the love of God, which is in Christ Jesus our Lord. (Romans 8:32-39, NASB)
Here we are told that nothing can separate us from the love of God which is in Christ Jesus. And the nothing must include “we ourselves” once we have put our trust in the Savior.
As for the passages that speak of “remaining in Him,” these passages are speaking about fellowship and not our judicial standing or relationship with God. As those who are born again or regenerated by the Spirit into the family of God, we stand in the perfect merit and grace of the Savior as justified sinners (see Rom. 5:1f). But as God’s children, we need to walk in fellowship with Him. This idea of fellowship is expressed, especially by John, with the word “abide” or “remain,” which is the Greek meno, “to abide, dwell, live, remain.” Our refusal or failure to abide in fellowship with Him means the loss of His abiding in us in the sense, not of His presence, but of His intimacy, control, and ability to direct our lives.
Amos 3:3 says, “Do two men walk together unless they are agreed?” The answer, of course, is no. This question, along with the others posed by the prophet Amos in this passage, are designed to show how Israel’s sin had separated her from fellowship with God and would bring them under judgment or discipline. As the Psalmist put it, “If I regard iniquity in my heart, the Lord will not hear (listen) to me.” Known sin in our lives quenches and grieves the Spirit, thus hindering our fellowship with His Lord. Our relationship with Him, however, is permanent.
I think this is precisely the issue in the book of 1 John, which I believe gives us a number of tests, not as proofs of salvation, but proofs (tests) of fellowship, or of an intimate knowledge of the Lord, who as light, wants to shine into our lives and lead us to experience His life. There the author uses the words “abide” and even “know” in this sense. We can know God personally as our Savior, but those who walk rebelliously in sin are failing to know Him intimately in the sense of fellowship. As an illustration of this, see John 14:8-10. In this passage the Lord uses both of these words, but He uses them in the sense of intimacy. They all knew Him, but not as deeply as they needed to know Him and would later in their relationship with Him, especially after the coming of the Spirit (see John 16:12f).
These issues are covered in the ABCs for Christian Growth series. I would also recommend Joseph Dillow’s book entitled, The Reign of the Servant Kings.