My understanding of abiding IS INDEED found in the Bible. I have quoted the verses numerous times. They are 1 John 2:17, 1 John 3:6, and John 15:6. If you can't see this, I can think of no other reason than what is spoken of in 2 Corinthians 4:4; maybe also 1 John 4:5-6.
OK, I am going to quote each verse and show you WHY your view is in error.
1 John 2:17 - The world and its desires pass away, but whoever does the will of God lives forever. NIV In this verse, the word "abides" means "live", obviously. We know the will of God from John 6:40 - For my Father’s will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day.”
1 John 3:6 - No one who lives in him keeps on sinning. No one who continues to sin has either seen him or known him.
This verse proves your error in what "abiding" means. If it meant to be "saved", then every saved person would "keep on sinning", but we know better. No believer achieves sinless perfection after salvation. And this verse doesn't teach it either.
John 15:6 - If you do not remain in me, you are like a branch that is thrown away and withers; such branches are picked up, thrown into the fire and burned.
It's never wise to use metaphors or figures of speech to formulate doctrines.
The beginning of this chapter is about fruit bearing, not how to get or stay saved. If a believer is out of fellowship by grieving or quenching the Spirit, how can they bear fruit? It's impossible. That is the Lord's point here. How can you disagree with this fact?
The better understanding is that those who have fellowship (intimacy, meaning they AREN'T grieving or quenching the Spirit) "keeps on sinning". Doesn't that sound much more reasonable than every saved person ceases to sin?
The last part of the verse indicates that the believer who does continue to sin doesn't really know (intimately, you know, fellowship) Him. They sure aren't having fellowship when they are grieving and quenching the Spirit.
Seems to me your understanding of "abide" is about maintaining relationship with God. But how is it possible to maintain relationship with your parents? That relationship cannot be changed or ended.
What does need to be maintained is fellowship with God. Which is only possible through confession for forgiveness of sins and purification of all unrighteousness, and being filled with the Spirit and walking by His means.
Your view leads to the false idea of sinless perfection. My view includes all the facts of Scripture about fellowship with God for fruit bearing, by being filled with the Spirit and walking by His means, and NOT grieving or quenching the Spirit.
This is why explanation is so important.