No they are no longer saved as both Romans 11 and Matt 18 and Ezek 18 all point out - OSAS is not a Bible doctrine.
Since our salvation was not initiated by us, was not bought by us, and is not held by us, how can it be ours to lose?
Rather than ask if man can lose his salvation, you should be asking if Christ is able to lose any the Father has given Him or is unable to keep us from falling.
You seem to misunderstand the Biblical doctrine of eternal security.
You talk about the Biblical doctrine of eternal security as if it's something we earn after salvation by proving ourselves worthy.
That's not the case at all. We're not saved by our own righteousness, but by Christ's righteousness, and our salvation is not kept by our faithfulness, but by Christ's faithfulness and ability to keep that which the Father has given Him.
If one is born again, then his salvation is secure in Christ's hands.
I would encourage you to think long and hard about the consequences of rejecting the Biblical doctrine of eternal security for a moment. If we could really lose our salvation, then
Hebrews 6:4-6 says that if we ever sin after being saved, we'll be lost forever with no way back, because the Lord would have to be crucified all over again to retrieve us. That means that it would only take one sin to fall away.
To deny the Biblical doctrine of eternal security, you must believe that, if one sin before we're saved was enough to condemn us, one sin after we're saved is enough to condemn us, as well. Doesn't this make the New Covenant worse than the Old? Under the Old Covenant, the Israelites were condemned for their actions, but we'd be condemned for our thoughts.
Under the Old Covenant, under the law, the Israelites couldn't murder. We can't even be angry. They couldn't commit adultery. We can't even have a lustful thought. If you're right, then we lose our salvation by doing less in following the law than the Israelites did under the law!
Is this really the Good News of Jesus Christ? Are these the riches of His Grace, that we have to live in fear of sinning? Are we saved by grace only to be placed under the constraints of an even more severely administered law?
But, back to your question, there are a host of verses that support the Biblical doctrine of eternal security.
Let's start with the most obvious:
John 6:35-40 says 35Jesus said to them, I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst. 36But I said to you that you have seen me and yet do not believe. 37All that the Father gives me will come to me, and whoever comes to me I will never cast out. 38For I have come down from heaven, not to do my own will but the will of him who sent me. 39And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day. 40For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.
So, here we have three promises:
a) That Jesus will not lose those the Father has given Him.
b) That Jesus will not cast out any who come to Him
That precludes both the sinner losing his salvation and Jesus taking his salvation away. So what means is left to lose salvation?
c) That God has already promised they would be raised on the last day.
Does God now break His promises?
And that's only the beginning. There is plenty of evidence for the Biblical doctrine of eternal security after that. For instance...
Romans 8:29-30 says that God predestined those whom He foreknew to be conformed to the image of Christ. If we can lose our salvation and, thus, our conformity to the image of Christ, then does this mean that God's foreknowledge is wrong? That's open theism, which has historically been condemned as heresy by the Church.
Jude 24 says that Christ is able to keep us from falling? If we can lose our salvation, does this mean that Christ is able to keep us from falling, but is merely unwilling? How is that consistent with the Biblical description of Christ?
Colossians 3:1-4 says that if we have been saved, we will appear with Christ in glory? It doesn't say "you might appear with Christ in glory, if you don't lose your salvation". It says "you will appear with Christ in glory". Done deal.
Philippians 1:6 says that if Christ has begun a good work in us, that He will finish it. How does He keep that promise to finish the good work He began in you, if you can lose your salvation?
1 Peter 1:23 tells us that when we are born again, we are born of incorruptible seed? If we can lose our salvation, then this seed is corruptible and that promise is not true.
Like
Colossians 3:1-4,
1 John 3:2 says that we are sons of God now and that when Christ appears, we will be like Him. There is no qualifier. There is no "...if we don't lose our salvation". And if we're sons of God, when has God ever disowned a son?
Titus 1:2 says that God has promised us eternal life and that He never breaks a promise.
In
John 10:27-29, Jesus promises us that He has given us eternal life, that we will never perish, and that we are not only in His hands, but in the Father's hands. How is Jesus' promise in
John 10:27-28 consistent with the idea that we can lose our salvation? Is Jesus really incompetent to keep those whom the Father has given Him?
John 5:24 says that if we are saved, we will not come into condemnation but will have eternal life? How can Jesus promise that we will not come into condemnation if He knows we can lose our salvation?
Romans 11:6 tells us that salvation is not by works. If we cannot be saved by works, then how can we lose our salvation by works? Furthermore, why isn't keeping our salvation a work?
John 14:16-17 tells us that when we are saved, the Holy Spirit indwells us forever. How can the Holy Spirit indwell in us forever if we lose our salvation? Since when does the Holy Spirit dwell in the unsaved?
Ephesians 1:13, 4:30 tells us that we are sealed unto the day of redemption. If we lose our salvation, then how can we still claim to be sealed?
1 Peter 1:4 says that our salvation is "imperishable, undefiled, and unfading". If our salvation is imperishable, how can we lose it? If our salvation is promised by God to be undefiled, how can we defile it?
It's been my experience that where you find a denial of the Biblical doctrine of Eternal Security, just scratch the surface and you'll find a belief in works-righteousness.
Again, I ask, is this really the Good News of Jesus Christ? Are these the riches of His Grace, that we have to live in fear of sinning? Are we saved by grace only to be placed under the constraints of an even more severely administered law?