Question: If a person loses their salvation by willful acts of sin, what of verses such as Hebrews 6:6, which state that should a person fall away, they cannot be renewed again to repentance?
Answer: I would view Heb 6:6 in the same way I would view the blasphemy against the Holy Spirit (Mat 12:31), the sin unto death (1Jn 5:6), which we are instructed to not pray for.
I would hold that the Bible teaches this is a state that a person can get themselves into by consistent rejection of God to the point where they have so hardened their hearts that the Holy Spirit can no longer deal with them.
None can come to Christ except that God draw them by the Spirit (Jn 6:44). If they have so hardened their heart to the point that the Spirit can no longer deal with them, then there is no way for them to be saved.
In Mat 12:22-32 we have the account where Jesus cast out the devil of a man that was blind and dumb, and healed him. The Pharisees who were present were so deceived and had their hearts so hardened that they could be in the presence of God incarnate, see Him perform a notable miracle of healing, and attribute this to the working of the devil.
I would hold that the reason there was no forgiveness for this blasphemous state of deception was because the Spirit of God could no longer penetrate their hardened hearts and convict them of their sins.
Hence, in 1Jn 5:6 we are told that there is no reason to even pray for those who sin a sin unto death.
In Heb 6:4-6, I would hold that those who have fallen away to the degree that it is impossible to repent have likewise sinned a sin that is unto death and have entered a blasphemous state of deception where the Spirit of God is unable to bring conviction to their hardened hearts.
I would like to also add that anyone who is in this state will have no concern for their soul at all and will only scoff at the claims and works of Jesus, as did the Pharisees who held Jesus was operating under the power of Beelzebub, the prince of the devils.
So to answer your questions, I would say if a Christian sins willfully or commits a known sin, they are separated from God in that sin brings spiritual death (separation).
While committing willful or known sin is like a dog going back to its vomit, a pig going back to wallow in the mire (2Pe 2:22), and counting the blood of Christ as an unholy thing (Heb 10:29), if a person will have godly sorrow for their wickedness and repent (2Co 7:10), there is forgiveness (1Jn 2:1).