We believe that Jesus died for all our sins, past and future, so why do we need to keep asking to be forgiven if Jesus already died to forgive that sin?
The general belief, that I think applies to most Christians, is that Jesus' death and resurrection opens the gates of heaven, saving us from sin in general, but that we must still choose to actually enter through the gate -- to repent of our individual sins and desire to sin no more.
To put it another way, Jesus' death makes repentance and forgiveness effective. Without His death and resurrection, repentance and forgiveness accomplish nothing.
Though each major tradition may have a slightly different basis for coming to this conclusion, it's easily validated by the oft-quoted John 3:16, particularly if taken with a little more of its context.
16 For God so loved the world that he gave his only Son, so that everyone who believes in him might not perish but might have eternal life. 17 For God did not send his Son into the world to condemn the world, but that the world might be saved through him. 18 Whoever believes in him will not be condemned, but whoever does not believe has already been condemned, because he has not believed in the name of the only Son of God. (John 3:16-18)
Emphasis is mine. And really, the whole thing could be emphasized, because the general point is that Christ's salvation, though universal, is only effective for those seeking and trusting in it.
Another explanation, coming from the Reformed tradition, is this: Christ died only for His people, not for all people. Various passages that support this are Matthew 1:21, John 10:7-18, John 17, and Romans 8:30. The idea here is that Christ's death does not make justification possible for His people - it actually effects justification for His people. And, since Christ did not die for everyone, those for whom Christ did not die must pay their own penalty.
In this view, Christ's death, all by itself, pays the penalty for the sins of His people. There's nothing added to it, not even our faith. This accomplishes the work of justification. Now, the Reformed position would also add that justification will always result in sanctification (faith without works is dead). However, the Reformed position is always very careful to add precisely nothing to Jesus' work in our justification.
We must still ask for forgiveness of our sins, because that is one vehicle through which God has ordained that our sanctification should take place. God is not just interested in delivering us from the guilt of our sin (done by Jesus' death on the cross), He also wants to deliver us from the power of sin. That's sanctification.
It is important to understand the difference between sin and sins. We have sin, and we are sinful. We also commit sins.
Our state of being sinful results in us being under a just condemnation in the sight of God. God, however, removes this condemnation and the penalty of our sign through our faith in Jesus.
Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God. John 3:18 ESV
Christ redeemed us from the curse of the law by becoming a curse for us—for it is written, “Cursed is everyone who is hanged on a tree”. Galatians 3:13 ESV
So, Christ's work on the cross and our faith in His finished work takes care of the penalty of sin. However, we still commit sins. This does not impact our destiny, but it does impact the intimacy of our relationship with God. Through faith, we are born into the family of God, and we will forever be sons and daughters of God. The relationship remains, but the intimacy suffers when we sin.
This is true in our relationships with each other as well. I will always be my father's son, but sometimes we have to ask forgiveness from each other to restore intimacy.
Although Jesus died for the sins of "the whole world" (1 John 2:2), the whole world does not get the benefits of His death unless it follows the condition, specifically, acknowledging their need of forgiveness of sins from God. With this statement of faith, that I have sinned against God and I need forgiveness from God through Jesus Christ, I am saved from my sins. Without that step of faith, the Lake of Fire awaits.
Why must I still ask for forgiveness when I sin again? It is the natural thing in normal life to say, "Oops, sorry about that," when we bump into someone, or to say something more substantial when we've hurt another. Confessing your wrong to God and others is your way of saying that you want to put it right, and you are accepting responsibility for your actions. There is nothing "mystical" about it; couples make up when one admits fault and sincerely makes it right, and it works in the spiritual sphere as well, though we call it confession and repentance. It's expected with our confession that we'll also take steps to make it right, as we see in 2 Cor. 7:9-12, in which Paul approves of the steps of repentance that were made.
If Jesus saves us from our sins, but we prefer to sin, what are we saying about our salvation? What are we saying about the gospel of our Savior?
Confession is so important because we need to call our sin what it really is or we will not deal with it on Christ's terms. If we call sin a "mistake," then we may not take hold of the benefits of our salvation, which is the blood washing away our sin, and seeking the power of the Holy Spirit to enable us to change the habits of sinful ways. See Psalm 15, which paints a portrait of one who is able to approach a holy God, and you'll find one trait is "speaking the truth in his heart" (rather than using euphemisms to lighten the severity of the problem within).
Psalm 51 is a terrific example of a prayer of confession, where David not only sees that he is wrong, but needs restoration from God for what sin did in him, and seeks to do better as a result.