The questioner also comments:
The consensus seems to say that it is sin that continues in the knowledge of the sin. Eventually God gives up. I think I disagree. The passage seems to be referring to something more specific. I think it may be denial of God. What do you think?
I think in many cases, the sin that leads to death, is denial of God. The explanation to a particular verse is often found in the same chapter or surrounding chapters. If you look at the next verse to the one you have quoted, we see that everyone born of God, does not make a practice of sinning. So, although those born of God will sin through weakness, their desire is to not sin.
Going back a few verses in the same chapter, we read that those who have life are those who have Jesus. Those who don’t have Jesus don’t have life. The reason we have life if we have Jesus, is because we live for and serve God and Jesus and the blood of Jesus cleanses us from our sin. We believe God, and therefore obey him, like Abraham (Romans 4:7). Those who don’t believe what God says, effectively deny his existence. As John 5:10 says:
Whoever does not believe God has made him a liar, because he has not believed in the testimony that God has borne concerning his Son.