The doctrine of eternal security as you call it. Is this a Biblical doctrine in terms of "once saved always saved".
It is synonymous. The problem here is not semantics. The problem here appears to be your misunderstanding of the atonement.
From the standpoint of God's perfect plan, He most certainly does not lose any who go astray. He does go out and find them and bring them back to the fold.
And this is the Eternal Security bit in a nutshell. If you are a Christian, you will persevere. Eternal Security does not mean live however you want and still be saved. Eternal Security means God will work in your to the point of perseverance because the good work that He began in us He has also promised to complete.
But the crucial problem with this so called Biblical doctrine is SIN.
We are not talking about going astray, we are talking about wilfull disobedience (sin).
Hebrews 10:26-27 "For if we go on sinning willfully after receiving the knowledge of the truth, there no longer remains a sacrifice for sins,"
This person is not a Christian. This person is not under the blood of Christ. He is still marred with the stain of sin. He has not been cleansed. He has not been justified. He does not have an Advocate. He was never a part of the flock. This is why he has no remorse and is still viewed by God as sinful instead of as one wearing the robes of Christ, the spotless Lamb.
This is as clear as a bell, sin willfully with no repentance and there comes a time when the sacrifice is no longer available.
The person sinning previously was under grace but later they were not. It is useless to imagine that the person was originally not a Christian. Because the person was under the sacrifice for sins.
And this is where the misunderstanding of the atonement kicks in. 1 Peter 3:18 is crystal clear that Christ died once for all. There is no repetitious sacrifice as the Catholic Mass is all about. Christ is not being sacrificed day in and day out for the purpose of sins. He died once, was resurrected once, and atoned the sins of mankind once. It was a complete act of perfect sacrifice never again to be repeated. If one was ever cleansed by the blood of Christ, he need fear not ever falling from grace. However, if he does "fall from grace," he was never really under grace and was never cleansed by the blood of Christ to begin with. He was only confused about his position as a child of God because the Spirit never regenerated him, caused him to die to self, or caused him to rise in Christ. Simply put, his sins were never atoned for and he was never under the sacrifice.
Theology is no shield against this clear warning. God's plan was perfect, man's response of course is imperfect. Look hard and long at church history, it is full of division.
This statement puts man over God. This statement makes man more powerful than God. This statement makes Christ an afterthought. This statement makes Christ a remedy to a bad situation instead of Christ being the reason for everything. This statement makes God a butler cleaning up a mess. This statement rejects God's sovereignty. This statement just is not Biblical.