Does Jesus’ blood continually cleanse us from all sin?
The Bible says we will give an account of our life and sin, but God washes away our sins at baptism and the blood of Christ continually cleanses. He forgives us and remembers no more, so is there judgment where our sin is remembered, or are we as white as snow because of Jesus' blood and our faithful obedience?
"If we say that we have fellowship with Him and yet walk in the darkness, we lie and do not practice the truth; but if we walk in the Light as He Himself is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin" (I John 1:6-7).
Notice that you did not quote this verse correctly. It does not say that the blood of Christ continually cleanses us from all sin. If it continually cleansed us from all sin, it would make us free to sin without any sort of remorse or consequence. "What shall we say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it?" (Romans 6:1-2). Jesus' death and the blood that was spilled to save us from sin. By his grace, the world can be healed from its state of death. "And He Himself bore our sins in His body on the cross, so that we might die to sin and live to righteousness; for by His wounds you were healed" (I Peter 2:24; refer also to Romans 6:3-7).
A "non-stop" cleansing was never mentioned. Can Jesus cleanse us from all sin that we currently have? Yes! But we must walk in the light (stop sinning) and ask to be cleansed. "But if we walk in the Light as He Himself is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin. If we say that we have no sin, we are deceiving ourselves and the truth is not in us. If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness. If we say that we have not sinned, we make Him a liar and His word is not in us" (I John 1:7-10)
Confessing our sins is a requirement to be forgiven after becoming a Christian. It is true we will give an account for everything we do, but luckily for us, we have Jesus as our advocate to the Father. "My little children, I am writing these things to you so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous; and He Himself is the propitiation for our sins; and not for ours only, but also for those of the whole world. By this we know that we have come to know Him, if we keep His commandments" (I John 2:1-3).
We are barely saved, in the sense that it is not some work of our own making that saves us but Jesus' sacrifice on the cross that allows us to enter heaven. Hence, when Judgment Day comes, we can have confidence, but only if we do what is right. "For it is time for judgment to begin with the household of God; and if it begins with us first, what will be the outcome for those who do not obey the gospel of God? And if it is with difficulty that he righteous is saved, what will become of the godless man and the sinner? Therefore, those also who suffer according to the will of God shall entrust their souls to a faithful Creator in doing what is right" (I Peter 4:17-19).
God can forget all the evil we have done once we are cleansed. But we need to remember that He can also forget all the righteous acts we have done if we turn back to evil.
"But when a righteous man turns away from his righteousness, commits iniquity and does according to all the abominations that a wicked man does, will he live? All his righteous deeds which he has done will not be remembered for his treachery which he has committed and his sin which he has committed; for them he will die" (Ezekiel 18:24).
We cannot store up righteousness, so we can do evil later in life. We live for the Lord until we die. If we turn against God in our life and die while in a state of unrighteousness, we will pay the penalty for our sins. "And you, son of man, say to your fellow citizens, 'The righteousness of a righteous man will not deliver him in the day of his transgression, and as for the wickedness of the wicked, he will not stumble because of it in the day when he turns from his wickedness; whereas a righteous man will not be able to live by his righteousness on the day when he commits sin.' When I say to the righteous he will surely live, and he so trusts in his righteousness that he commits iniquity, none of his righteous deeds will be remembered; but in that same iniquity of his which he has committed he will die" (Ezekiel 33:12-13; refer also to Romans 2:1-16).