“Why...or how?”
Righteousness is a forensic term, derrived from the same root as justification. It means that God will judge right which He did with Jesus. From that flows that all who have trusted Jesus for salvation have been judged in Jesus as innocent; not, not guilty, which implies that there is not enough evidence of what did or can take place; but innocent, no more condemnation. They can’t lose that judgment since it is based on the faithfulness of God to His covenant; i.e. His righteousness.
The fifth canon of the Remonstrance says that man can lose that judgment of innocent or “rightness”. If that be so then God cannot be righteous since His judgment is conditional; based not on the efficacy of what Jesus did, but on the ability of man to hold on; a kind of probation period. That is not being faithful to His promise.
Article 5
That those who are incorporated into Christ by true faith, and have thereby become partakers of his life-giving Spirit, have thereby full power to strive against Satan, sin, the world, and their own flesh, and to win the victory; it being well understood that it is ever through the assisting grace of the Holy Ghost; and that Jesus Christ assists them through his Spirit in all temptations, extends to them his hand, and if only they are ready for the conflict, and desire his help, and are not inactive, keeps them from falling, so that they, by no craft or power of Satan, can be misled nor plucked out of Christ’s hands, according to the Word of Christ, John 10:28: “Neither shall any man pluck them out of my hand.” But whether they are capable, through negligence, of forsaking again the first beginning of their life in Christ, of again returning to this present evil world, of turning away from the holy doctrine which was delivered them, of losing a good conscience, of becoming devoid of grace, that must be more particularly determined out of the Holy Scripture, before we ourselves can teach it with the full persuasion of our mind.
There are certainly scriptures that cast doubt on the question. "4For it is impossible, in the case of those who have once been enlightened, who have tasted the heavenly gift, and have shared in the Holy Spirit, 5and have tasted the goodness of the word of God and the powers of the age to come, 6and then have fallen away, to restore them again to repentance, since they are crucifying once again the Son of God to their own harm and holding him up to contempt. 7For land that has drunk the rain that often falls on it, and produces a crop useful to those for whose sake it is cultivated, receives a blessing from God. 8But if it bears thorns and thistles, it is worthless and near to being cursed, and its end is to be burned." - Hebrews 6
I haven't studied it, and wouldn't want to commit one way or the other. Neither did the Arminians of 1610...