Base on the context, a real believer could not do the falling away. Hebrews 6 speaks rather of impossibility than possibility. There’s no way a real born again (saved by the grace of God) will again be born again. There is no such thing as born again and again and again. The relationship has been firmly grounded in Christ. What the believer received from Christ then no one is able to pluck them out of his Father’s hand especially when it has been sealed by the Holy Spirit. The real believers are saved, secured and sure serving Christ. Context in Hebrews speaks of receiving blessing from God and things that accompany salvation (v.7), this is referred to the good works or labor of love shown toward the brethren but this ministry may be lose and be rejected but then again it does not say about the losing of salvation. It is rather a of a losing of rewards to those who fall back into this ministry and be held accountable during the Judgement Seat of Christ (JSOC) where our works good or bad will be tested by fire. So, it is the desire of the writer of the Hebrews, if not Apostle Paul to shew the full assurance of hope until by patience receives the blessings. (vv. 10-12).
2Co 5:10 For we must all appear before the judgment seat of Christ; that every one may receive the things done in his body, according to that he hath done, whether it be good or bad.
Rom 14:10 But why dost thou judge thy brother? or why dost thou set at nought thy brother? for we shall all stand before the judgment seat of Christ.
Rom 14:11 For it is written, As I live, saith the Lord, every knee shall bow to me, and every tongue shall confess to God.
Rom 14:12 So then every one of us shall give account of himself to God.