A Question From A Reader (UPDATED)

Why are we told to ask forgiveness for our sins on an ongoing basis (Luke 11:4, when we have already been declared righteous?

First of all we must distinguish between the forgiveness of sins and justification. Not separate them, but properly categorize them.
The forgiveness of sins refers to an act whereby God removes the guilt of sin based upon Christ's death. This leaves us as though we were innocent.
Justification refers to a declaration of righteousness. This declaration is based upon the His forgiveness of our sins and the righteousness of Christ which is imputed to our account. So we are declared to be righteous, and not merely innocent.
Forgiveness of sins (the imputation of our sins to Christ's account for which He suffered on the cross) is the negative aspect of our justification, where the imputation of Christ's righteousness is the positive aspect.

Now, just as we understand that our the declaration that we are positionally righteous does not mean that we are practically righteous (simul justus et peccator, simultaneously righteous and a sinner), neither does the forgiveness of sins mean that we in ourselves are free from the presence of sin.
So as we must continue to strive unto 'good works' (righteousness), we must also daily repent of sins. As we must continually believe the Gospel, we must also continually be 'transformed by the renewing of our minds'. (Rom 12:2)
In the email I sent to this reader I made this statement which he asked me to clarify;

Sins are not forgiven until we ask for forgiveness for those sins. Even though all sins are paid for by Christ's death, they are not forgiven at the time of Christ's death. Sin is not forgiven until we ask for forgiveness based upon Christ's death.

Well, for starters, this is true of our initial conversion experience, isn't it? Although Christ's atonement paid for all the elect's sins (past, present, and future), forgiveness for those sins was not obtained until we came to Christ. So there is a difference in what has been paid for and what has been obtained. When we come to Christ repenting of our sins, we are forgiven for those sins. But as each and every Christian knows, if they are honest, they have not lived sinless lives after their initial conversion. While God already knew those sins that we would commit after conversion and punished Christ for them, forgiveness for those sins, although paid for, is not obtained until we repent of those sins.

Salvation is Scripture is revealed to us in three tenses; I have been saved, I am being saved, and I will be saved. These three tenses correspond with our justification, sanctification, and glorification. I am declared to be righteous upon the merits of Christ. I am also being made righteous by the inward work of the Holy Spirit through the ministry of the Word. I will finally be both positionally and practically righteous when I see Christ on the resurrection day.
Put another way, I have been placed in Christ, I am being conformed to His image, and I will be like Him.

This means that just as repentance of sins and faith in Christ result in justification, they will also result in sanctification, and ultimately glorification. So we are commanded to continually ask for the forgiveness of sins, not for our justification, but our sanctification, which we trust will eventually result in our glorification.

(Update) Recommended Reading: Taste and See, Chapter 29 "Justified, But Not Forgiven?", by John Piper.