Hebrews 6:4-12 For it is impossible for those who were once enlightened, and have tasted¹ of the heavenly gift, and were made partakers² of the Holy Ghost, 5 And have tasted the good word of God, and the powers of the world to come, 6 If they shall fall away³, to renew them again unto repentance; seeing⁴ they crucify to themselves the Son of God afresh, and put him to an open shame. 7 For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: 8 But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned. 9 But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak. 10 For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister. 11 And we desire that every one of you do shew the same diligence to the full assurance of hope unto the end: 12 That ye be not slothful, but followers of them who through faith and patience inherit the promises. (KJV)

1. Matthew 27:34 they offered him wine to drink, mixed with gall; but when he tasted it, he would not drink it. (NRSV)

2. Matthew 7:21-23 "Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only the one who does the will of my Father in heaven. 22 On that day many will say to me, 'Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many deeds of power in your name?' 23 Then I will declare to them, 'I never knew you; go away from me, you evildoers.' (NRSV)
Remember even Judas healed and cast out Demons in Matthew 10:1-2. Some of the people who saw the miracles, were healed themselves or healed in the name of Jesus, still rejected him, and so were never saved.

3. This word in Greek is parapipto which properly means, "to fall in one's way" (para, "by"), signifies "to fall away" (from adherence to the realities and facts of the faith), not apostasia which means "a defection, revolt, apostasy," is used in the NT of religious apostasy; in Acts 21:21, "you teach apostasy from Moses." So this speaks of some one who now understands about Christ but continues to reject him.

4. "Seeing" is not in the Greek, it is supplied by the translators and should be translated "While."
Examples of "while" being inserted to get across the whole idea are:
Matthew 25:10 And while they went to buy it, the bridegroom came, and those who were ready went with him into the wedding banquet; and the door was shut. (NRSV)
Galatians 2:17 But if, while we seek to be justified by Christ, we ourselves also are found sinners, is therefore Christ the minister of sin? God forbid. (KJV)
2 Peter 2:13 suffering the penalty for doing wrong. They count it a pleasure to revel in the daytime. They are blots and blemishes, reveling in their dissipation while they feast with you. (NRSV)
2 Peter 2:19 While they promise them liberty, they themselves are the servants of corruption: for of whom a man is overcome, of the same is he brought in bondage. (KJV)

Literally in Greek "While they crucify to themselves the son of God afresh" Meaning while they crucify to them selves (continue to reject Christ) They can find no other way of pleasing God not even going back into Judaism.
The parable of the sower from Luke 8 is alluded to here. The nature of someone who is bad ground, never changed, so they will never find salvation because there is no other except Christ.
Verse 9 states that Paul knew those he was talking to were not in this category because their nature had been changed, they were born again.