"Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new." (2 Corinthians 5:17)
When Jesus died on the Cross, and then He was raised from the dead three days later, He took us out of our dead selves in Adam, and gave us new selves, a new life in Himself (Ephesians 2:4-6).
We are no longer dead in Adam, but alive in Christ Jesus:
"For if by one man's offence death reigned by one[Adam]; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ." (Romans 5:17)
Righteousness is an immutable gift which we receive, and keep receiving, through Christ Jesus.
We need to understand that Jesus did not just take our unrighteous stance before God.
"For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5:21)
He became sin, which means that He took our sin, and therefore we can never get back. He took our sins in His own body (1 Peter 2:24)
In turn, we were made the righteousness of God in Christ. Indeed, we receive and keep receivig His gifts of righteousness and grace, but righteousness defines who we are now today!
It's not something that can leak or fall away from us.
Consider what John the Beloved writes in His First Epistle:
"Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous." (1 John 3:7)
"Doing righteousness" is all about believing on Jesus!
"Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent." (John 6:29)
When we believe on Jesus, this is what happens:
"Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not. 2Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is." (1 John 3:1-2)
We are as righteous as Jesus! John could not have said it more clearly:
"Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world." (1 John 4:17)
We have righteousness, not just as a part of us, but it defines who we are in Christ Jesus.
Righteousness is our new identity, since Christ has been made our righteousness (1 Corinthians 1:30)
We are are new creation in Christ Jesus, defined by His gift of righteousness, something that cannot change, whether we fail or fall, whether we sin or win.