Why should believers continue to repent of our sins if we are already forgiven?
Sin is the transgression of God's law (1 John 3:4). James 2:10 says, 'whosoever shall keep the whole law, and yet offend in one point, he is guilty of all'. If you break God's law once you are under its curse as Galatians 3:10 says, 'For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them'.
1 John 1:6-7 If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth: (7) But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
If we claim to be Christians but are constantly walking in darkness, our profession is a lie. It is also teaching that if we do walk in the light, it is a proof of our union with God. Our union with God is made evident by the effect.
But is this teaching perfectionism? No, it is teaching a style of life which comes from your conversion as you conform to the image of His Son.
John was writing to saved believers with the purpose 'that ye may know that ye have eternal life' (1 John 5:13) and yet he asks recipients of salvation to ask for forgiveness. The forgiveness of sins which verse 9 speaks of isn't the act of forgiveness by God in our relation to God by being reconciled by justification which is done at once, and includes all sin, past, present, and to come; but is to do with our fellowship with God which is strained by sin, and how disobedience harms our walk with God.
Walking in the light of Christ, being more aware of your sin and continual repentance are evidences of your salvation which John spoke of in his epistle which had the purpose of assuring the believers of their salvation. The child of God is to become more and more aware of their sinfulness and not boasting in some kind of imagined perfection.
John 10:27-28 My sheep hear my voice, and I know them, and they follow me: (28) And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
John 6:47 Verily, verily, I say unto you, He that believeth on me hath everlasting life.
What does everlasting mean? Forever or until the next time you commit a sin? Salvation is all God's work and not our own. Not only that, the scriptures teach that the believer is already in this life in possession of salvation and eternal life (John 6:47).