The Lord knows the heart of all men (1 Chron.28:9) so he knows who has true faith and who doesn't. And to those with true faith He gives eternal life.
It's quite interesting that you pick that verse to cite. It says the Lord SEARCHES the hearts and UNDERSTANDS THE INTENT of the thoughts, but it refutes the idea that God knows Solomon's future heart and thoughts. I'll quote it fully here:
[1Ch 28:9] 9 And thou, Solomon my son, know thou the God of thy father, and serve him with a perfect heart and with a willing mind: for the LORD searcheth all hearts, and understandeth all the imaginations of the thoughts: if thou seek him, he will be found of thee; but if thou forsake him, he will cast thee off for ever.
Notice that it does NOT say that God knows at this time whether Solomon will forsake God or not, but IF he does, than God will cast him off forever. "Forsake" means "to quit or leave entirely; abandon; desert". You can't forsake something you didn't already have. So it refutes your claim that God knows all about Solomon's heart for the rest of his life, and that "believers" always stay believers. If it applies to our discussion of Christians (and some would say it does not, though I AGREE WITH YOU that it does), then God may "cast off forever" those that He determines TODAY are seeking Him, IF they forsake Him. To me that's an indication that salvation is a process--He starts and finishes our faith if we don't turn from Him.
[Heb 12:2 KJV] 2 Looking unto Jesus the author ("starter") and finisher of [our] faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God.
[Heb 12:7-8 KJV] 7 If ye endure chastening, God dealeth with you as with sons; for what son is he whom the father chasteneth not? 8 But if ye be without chastisement, whereof all are partakers, then are ye bastards, and not sons.
If we refuse chastisement (which is applied when someone doesn't do what God wants them to do), then that means we DON'T turn from our sins, and the author of Hebrews seems to think that means we are NOT sons.
So are you denying that the Lord does not know who has true faith? You have already confirmed that you believe that the Lord gives true believers eternal life. And you have confirmed that those to whom the Lord Jesus gives eternal life shall never perish.
Because true believers persist in their belief. Persistence in their belief, as far as I can tell, requires knowing what someone is going to do in the future. Free will requires that someone be allowed to change his mind. God either knows what a man is going to do for the rest of his life or He doesn't. If He does, then the man's future is locked in somehow--either because the future is fixed (and God can't even change it) or God makes us robots so we can't change. The second option is the only one that doesn't limit God. The second option does not allow for free will. Maybe that's ok when it comes to believers--believers will have handed their will over to God, to mold and shape it as He wants. If that's what "true belief" means, then the answer to your OP is there for you: belief in God requires people to fulfill what God wants them to fulfill, call it law or duty or the desire to do God's pleasure. And if God makes us robots after our conversion, so be it.
I explained this all to you before, Jerry. I'm fine if you don't accept it, but why don't you at least acknowledge that I said it and not keep asking me the same questions over and over?
With these facts in mind then address all of these "three" points and tell me why you believe that those who have been given eternal life can perish.
I dispute the term "have been given" as if it is a package that is handed to someone. All believers have been given eternal life. If they decide they don't want it, they can commit spiritual suicide, similar to what Adam and Eve did in the Garden. Just like King Solomon--he could seek God or not seek God. It wasn't one-time event, but a life-ling, continued choice to seek God or not. I don't really see much difference between that and the Christian life--a continued choice to seek God--we don't do it perfectly, we need to repent when we stop seeking Him, God is merciful if we decide to follow after the world once in a while, or even for years, but if we reject Him outright, even after we "believe", then I don't see how we still have eternal life.
I'll tell you what I think the difference is. Adam's sin caused us to need Christ's sacrifice. Adam's sin made us sin "naturally". Jesus fixed that problem with His death on the cross. Now we are freed from sin's curse and sin's bondage. We now have the ability to truly, freely choose whether we obey our master who bought us or deny Him (2 Pet 2:1). These are mere thoughts on the subject. I could be wrong. But it makes some sense to me.