Many people read this context and come to the conclusion that it means it is possible for someone to go so far down the road of sin that it impossible for them to come back to righteousness.  This is not at all what the writer is saying here. 

Hebrews 6:4-6 applies to those who are no longer capable of feeling remorse or guilt for their actions. Someone who does not feel remorse cannot repent. They have been Christians and know what it is like to be one but have made a conscious decision to forsake God.  Of great significance is the structure of the words within the context.  For this purpose we will use the ESV translation:

"For it is impossible to restore again to repentance those who have once been enlightened"

Notice it does not say it is impossible for them to repent.  What the writer's intent here is that once someone has made the decision to forsake Christianity, it is impossible for another Christian to say or do anything to restore them.  Macknight wrote that "The apostle does not mean that it is impossible for God to renew a second time an apostate; but that it is impossible for the ministers of Christ (to do so)."  At this point it is entirely up to the one who has fallen away to come to his senses and repent.  And if this is done, we have the assurance from God that if they truly repent, they will be forgiven and restored to a favorable standing in the family of Christ.

"since they are crucifying once again the Son of God to their own harm"

Christ was crucified to make forgiveness of sin available to all sinners.  That crucifixion was entirely on Him, at His discretion and if His own free will.  That crucifixion was a gift given to all mankind by Christ and as such, mankind is not held accountable for it.  In other words, God is not going to punish faithful Christians for the death of Christ.  On the other hand, the apostate who rejects that crucifixion literally throws that sacrifice back in Christ's face and he/she will bear the just punishment for His death.  That is one of the reasons why we see the warning Peter gave to apostates in 2 Peter 2:20-21

"For if, after they have escaped the defilements of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein and overcome, the last state is become worse with them than the first. 21 For it were better for them not to have known the way of righteousness, than, after knowing it, to turn back from the holy commandment delivered unto them." (ASV)

These two contexts, and others such as James 5:19-20 completely and utterly destroy the false Calvinistic doctrine of 'Once Saved, Always Saved' (OSAS).  If it were not possible for a Christian to fall away, then why are there warnings against it?  It makes no sense to warn a Christian against something that cannot happen.   The doctrine of OSAS is as counterfeit as it gets and has lulled countless people into a state of false security.

" and holding him up to contempt."  (ESV)

The Christian who rejects Christ, declares to the world that His sacrifice on their behalf is worthless to them.  Christ humbled Himself and unjustly died the death of a convicted criminal on the cross of Calvary to save an unworthy soul from their sin and they they reject that sacrifice of selfless love and throws it back in His face.   The Hebrew writer expounds on this in Hebrews 10:26-27

"For if we sin willfully after we have received the knowledge of the truth, there no longer remains a sacrifice for sins, 27 but a certain fearful expectation of judgment, and fiery indignation which will devour the adversaries." (NKJV)

Woe is the unwise soul who accepts salvation and then rejects it and never comes to repentance.