Justified, in regard to the verse above, means to be declared righteous or acceptable to God. Guilty humans at trial under a magnifying glass in a cosmic court need a verdict of "not guilty" in order to be freed from the consequences of sin. Without being justified by God they will be bound over to judgment, which in a cosmic context, unfortunately, can only be cosmically ultimate. For someone actually guilty (as are all humans before God) there can be no escape in such a court on the basis of technicalities, obfuscation, ignorance, prejudice or character (i.e. good works).
Faith, as used in the above verse and as generally understood as "saving faith", is an apprehension of who Jesus is and what he has done which moves a person to trust Christ as his or her savior and follow Christ as his or her leader. As long as a person has faith that Jesus came from God, died for his or her sins, rose bodily from the dead victorious over sin and death, and is his or her Lord, that person is justified without the possibility of change in status. However, if such faith is lost or reversed, then so too is the condition for justification, and hence salvation, and the result is apostasy or falling away. We can lose our salvation, therefore, if we lose our faith.
Works, as spoken about in that verse, are actions of mind or body which accrue toward the worker's justification. In this instance, they are specified to be in the context of the law, i.e. the Mosaic Code. However, works of the law cannot possibly effect justification because: 1) good works have no power to erase or nullify bad works; 2) even the works of law associated with sacrifices intended to remit sins cannot undo the sin nature of the sinner, which has him or her in sin, virtually, before the last whiff of smoke has dissipated; and 3) it is impossible for the blood of animals to cleanse a guilty human conscience. [How could they? Neither party (God or the sinner) has any "skin in the game."]
Since salvation is not founded upon nor attributable to works then neither can a loss of salvation be the result of such. Our works, in themselves, good or evil, do not have the power to engage, alter or to unravel what Jesus Christ has already done on the cross and in rising from the grave. Whereas keeping a clean conscience is a boon to faith, keeping or not keeping a clean conscience can neither keep one saved nor cause him or her to lose salvation. Sin, though it doubtless arises out of some sort of unbelief, cannot be the source of apostasy anymore than it is the source of salvation; otherwise, virtually every Christian would eventually apostatize.
Apostasy is departing from the faith. It starts with some disappointment or disillusionment with Christ and ends with one abandoning the trust he or she has in who Christ is and what he has done. If one does not trust in Christ as the Son of God, nor rely upon his death and resurrection for justification before God, that one cannot possibly be saved so long as he or she remains in such unbelief. It matters not that he or she believed at one time or even that he or she was baptized.
Sin is not and never can be the cause of apostasy! Faith is what effects justification, and a departure from faith is the only thing that could effect a loss of salvation.