This scripture cannot mean what you say it does when taken in context. As I understand your remarks you are saying the term "believe not" does not mean that our faith sometimes falters but that we can turn away from Him altogether and live a life of denying the faith without our relationship with Him being altered.
This is not true contextually. This verse with the one before it reads like this:
11 The saying is trustworthy, for:
IF we have died with him,
we will also live with him;
12 IF we endure
we will also reign with him;
IF we deny him,
he also will deny us;
13 if we are faithless, he remains faithful—
(2 Timothy 2:11-12)
Your interpretation of verse 13 it is contradicted by verse 12 which sets conditions on our future experience, conditions indicated by that very potent word IF. We will not live with Him forever IF we do not die with Him. We will not reign with him in the world to come IF we do not endure this world.
That verse 13 refers to God's continued faithfulness when we go through periods of doubt better fits the tone of an exhortation to endure that is intrinsic to this verse. The reason is that we are more likely, in times of testing, to go through periods of doubt. To keep us from being daunted by the task Paul adds that while we must endure and keep our faith absolute perfection is not demanded. When we waver God will still be with us.
However, the idea that our "faithlessness" means apostasizing from the faith is directly contradicted by the phrase "if we deny him, he also will deny us"
2 Timothy 2:11 It is a faithful saying: For if we be dead with him, we shall also live with him:
We are dead and our life is hid with Christ in God and when Christ appears, then shall we also appear with Him in glory (no doubt about it)!
Colossians 3:1 If ye then be risen with Christ, seek those things which are above, where Christ sitteth on the right hand of God.
Colossians 3:2 Set your affection on things above, not on things on the earth.
Colossians 3:3 For ye are dead, and your life is hid with Christ in God.
Colossians 3:4 When Christ, who is our life, shall appear, then shall ye also appear with him in glory.
2 Timothy 2:12 If we suffer, we shall also reign with him: if we deny him, he also will deny us:
This is about suffering, “If we suffer, we shall also reign with Him” as in:
Philippians 1:27 Only let your conversation be as it becometh the gospel of Christ: that whether I come and see you, or else be absent, I may hear of your affairs, that ye stand fast in one spirit, with one mind striving together for the faith of the gospel;
Philippians 1:28 And in nothing terrified by your adversaries: which is to them an evident token of perdition, but to you of salvation, and that of God.
Philippians 1:29
For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
Philippians 1:30 Having the same conflict which ye saw in me, and now hear to be in me.
If we deny Him the suffering, He also will deny us the reign!
2 Timothy 2:12 If we suffer, we shall also reign with him: if we deny him, he also will deny us:
It's about reward 1 Corinthians 3:10-15 KJV, 2 Corinthians 4:17 KJV, Colossians 3:24 KJV)
Knowing our position in Christ found in passages throughout Romans through Philemon including our being dead with Him and that we shall live with Him when He Who is our life appears: we believers read 2 Timothy 2:13 KJV as an “even if”! Even if we believe not, we are identified in and with Him. To deny us, would be to deny Himself and He cannot deny Himself as He abideth faithful!
Galatians 2:20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.