First I cannot understand why any believer would not confess his/her sin.
That being said I assume that you pointed to 1John 1:9 about confessing our sin but that passage is not speaking about the saved/a believer. That passage is speaking about the Gnostics who had crept in and making false claims one of which was they claimed they had no sin making them lost while they claimed to be right with God. If you notice it says this;
If we confess our sins, he is faithful and just to forgive us [our] sins, and to cleanse us from all unrighteousness
The saved are already cleansed and this passage is speaking to those who have not been cleansed and in this case the Gnostics. For the believer fellowship is never broken as some try and teach. In fact when we sin fellowship becomes alive to another level although usually not a pleasant one.
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I find it interesting that you consider the apostle John a Gnostic. John says we, so that the we would include John as one that had to confess His sins.
1 John 1: 6 If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth:
7 But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
8 If we say that we have no sin, we deceive ourselves, and the truth is not in us.
9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
10 If we say that we have not sinned, we make him a liar, and his word is not in us.
Verses 6 through 10 John says "WE" if we, so if the "WE" are Gnostics that would mean John was a Gnostic and had turned from the truth. Interesting teaching. In fact John says "WE" in almost every verse of the first chapter and starts off chapter 2 with 1 My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:
2And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
My little children this is definitely a reference to believers, John he wrote these things to you little children so you sin not. Sure appears this whole book is addressing believers. But maybe John was a Gnostic and none of us caught it before.