concerning eternal security
The key to the question of eternal security is 1 John 2:19, "They went out from us, but they did not really belong to us. For if they had belonged to us, they would have remained with us; but their going showed that none of them belonged to us." This verse shows us that like other doctrines, there is more than one side to the question. On the experiential side, the Church may see those who for all appearances have heard the Word of Life, believed, were saved, and then abandoned their faith. However, God does not judge on appearances (Matthew 7:21-27).
What is it that saves a man? Is it hearing and believing only? No, a man who has heard must then step forward in an active faith and follow after Christ. The application of the work of the Cross for salvation requires at least five distinct steps: One must believe in Christ (Acts 16:31; John 3:16), Repent of Sin (Acts 2:38; 3:19; 2 Corinthians 7:10), Ask for Forgiveness (1 John 1:9), Accept and Acknowledge Christ as Lord (John 1:12; Romans 10:9, 10), and Follow Christ (Luke 9:23; John 14:21).
It is apparent from the context where apostasy is dealt with that the apostates fell short of coming into the full grace of Christ. We see in Hebrews 3:7-4:11 that we have the warning not to be like those who rebelled by having an unbelieving heart that turns away from the living God. Scripture also says, "the message they heard was of no value to them, because those who heard did not combine it with faith." (Hebrews 4:2). And so it is clear that in this case, those with an unbelieving heart could not have once been in Christ because they did not have faith, and it is impossible to be saved without faith (Ephesians 2:8,9). Likewise in Hebrews 6:4-8, "It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, who have tasted the goodness of the word of God and the powers of the coming age, if they fall away, to be brought back to repentance, because to their loss they are crucifying the Son of God all over again and subjecting him to public disgrace. Land that drinks in the rain often falling on it and that produces a crop useful to those for whom it is farmed receives the blessing of God. But land that produces thorns and thistles is worthless and is in danger of being cursed. In the end it will be burned." Scripture first shows us the earthbound viewpoint. It appears to us that one might abandon his faith, but in reality, that person was not one of us; the one whose fruit is thorns and thistles was never saved. This is reinforced by Jesus' own teaching in Matthew 7:21-27; 13:1-23, where He shows that the one who is saved is the one who not only hears the word and responds but who also steps out in faith and verifies his faith by the Fruit of the Spirit (Galatians 5:22-25).
In view of the teaching of Scripture on this subject, there is no reason to doubt the promise of eternal life. When someone has truly come into Christ he has been saved - Eternally.