Whether a real Christian can fall away from the Lord is a very hot subject among Christians. One passage that we discuss is Hebrews 6. I can't speak to the whole question in just one short post, but I would like to comment on this passage, which I will break up into quotes below.
"Therefore leaving the elementary teaching about the Christ, let us press on to [c]maturity,"
This introduces the writer's goal -- he wants his readers to press on to full spiritual maturity. This shows the writer's shepherd heart. A true shepherd wants Christians to grow and become mature in their faith. In chapter 5, he had criticized the readers for lagging behind in maturity. Their immaturity was shown in their desire for simplistic, basic Bible teaching, plus a lack of discernment about good and evil (see 5:11-14).
"not laying again a foundation of repentance from dead works and of faith toward God, 2 of instruction about washings and laying on of hands, and the resurrection of the dead and eternal judgment."
The writer (probably Paul and Barnabas, in my opinion) had already thoroughly taught the readers very basic Christian teachings. Like a seventh-grade teacher who doesn't want to go back over the ABCs again, the writer didn't want to lay those basic foundations of faith with this congregation all over again. He wants them to move forward in knowledge and insight.
3 "And this we will do, if God permits."
We who are pastors should never forget that all of our successes in serving other people come with God's help. As the apostle Paul says elsewhere, "Who is adequate for such a thing?" 2 Corinthians 3:5.
4 For in the case of those who have once been enlightened and have tasted of the heavenly gift and have been made partakers of the Holy Spirit, 5 and have tasted the good word of God and the powers of the age to come,
Now, the writer speaks of a a special category of person. This is a person who has been once-for-all enlightened regarding the Gospel. This person has experienced the Holy Spirit. "Taste" means to experience; for example, Christ tasted death for every man (Hebrews 2:9). They have experienced blessings from God's good word (see Psalm 119:103), and the powers of the age to come This latter fact could refer to the ministry of the twelve apostles, who had ministered to the people of this congregation according to 2:3-4.
The writer is describing a non-believer who has experienced the gracious blessings of God and His word, and has fully, clearly understood the Gospel.
6 and then have fallen away,
To "fall away" is used of different types of people. Jesus said that a false convert will always fall away when persecution comes (Matt. 13:20-21). Jesus' disciples also fell away from Him on the night of His betrayal (Matt. 26:31), but, unlike the stony-ground hearer, they all immediately repented and came back.
it is impossible to renew them again to repentance,
Everything the writer describes embodies the renewing , prevenient influence of the Spirit of God on an unbeliever. Where once he was blind, the Spirit made him see that Jesus is the Christ. He experienced the blessed power of the Spirit, drawing him to repentance. It is impossible for him to be renewed by God again to repentance. Saving repentance was the goal, but a goal he never reached. Why is it impossible?
[d]since they again crucify to themselves the Son of God and put Him to open shame.
Because of the enormity of his sin against Jesus Christ. God shows abundant mercy to the spiritually ignorant, like Paul (1 Timothy 1:13). But when the spiritually-enlightened person still rejects Christ, it is as if they are siding with those who wickedly crucified Christ, which was the greatest sin of all history. It is as if they are driving the nails into His hands and feet all over again.
7 For ground that drinks the rain which often [e]falls on it and brings forth vegetation useful to those for whose sake it is also tilled, receives a blessing from God; 8 but if it yields thorns and thistles, it is worthless and close [f]to being cursed, and [g]it ends up being burned.
If an unbeliever responds back to the prevenient mercies of God with faith, which then by its very nature grows the good fruit of godliness, God blesses him or her. But if an unbeliever responds back to the prevenient mercies of God with full, conscious, willful unbelief and sin, he shows himself to be a worthless person (Matthew 25:30). God could curse that person on the spot, and in the end God will cast him into the lake off fire.
The Hebrews 6:4-6 person is a non-Christian who receives many renewing graces from God and then, fully enlightened, spits in Christ's face. This interpretation is further strengthened by the writer's following words, where he says he is convinced of better things of his readers, things that accompany being a saved person (6:9).
Verse 9 shows the group from verses 4-6 is a group different from the readers; and the reason the readers will not act that way is because they were saved people.