Of course. Even Judas was sorrowful over his sin, according to the Bible. The world is full of people who are disgusted at at least some of their sins, who seek to put particular sins behind them. This kind of sorrow is not how we have peace with God. While repentance is intimately connected to how and why God forgives us, it is not at all by itself a sufficient cause.
Properly speaking that repentance which “saves” is not merely a turning from, but is a turning to. We have peace with God because Jesus suffered the wrath of the Father that is due to us for our sin, and because He lived a perfect life. The work of Christ becomes ours when we, because of the work of the Holy Spirit in first regenerating us, repent and believe, or trust in the work of Christ. If we so trust all our sins are forgiven, because they have already been punished. This describes all our sins, past, present and future.
If our repentance includes turning to the finished work of Christ, if it includes trusting in His life and atoning death, the promise of God is that we will indeed be forgive (I John 1:9). Because His promises are true, we can and must trust them.
We do, of course, continue to sin. Satan, the accuser, delights to make much of this. He loves to rub our faces in our sins, to tell us that sinners such as we surely cannot be saved. If our response to this kind of assault is to deny the reality of our sin, he wins. If our response on the other hand is to wallow in our sin, he wins. The right response is, “I am a sinner. Worse even than you know Satan. But my Father sees me as pure and whole, a spotless bride, because He has dressed me in the perfect righteousness of His Son.” Telling the devil, “No, I am good” invites more attack. Telling the devil, “Yes, I am evil” only invites more attack. Telling the devil, “Jesus is righteous and I am in Him” will make him flee.
When we diminish our sin, we foolishly rest in ourselves. When we despair in our sins we foolishly diminish His grace. Our calling is to own our sin, to plum its depths, but then to know that God’s grace in Christ is greater still. Deep sorrow and repentance followed by deep confidence in His grace will lead to deep and immovable joy.
Continue to repent. We do so not because our future sins are not forgiven, but so that we might nor presume upon that grace, that we might rejoice in our forgiveness. Let us all, however, also continue to repent for our unbelief in His grace. When God says “I forgive you and I love you” to respond “I don’t believe you” is pure folly, To respond “I’m not worthy” is to belabor the obvious. To respond “Thank you” is to grasp the Good News.