In most cases, when one responds and asks the church to pray for them, I assume they have already prayed for forgiveness and are simply acknowledging that sin and asking for the forgiveness of the brethren for whatever reproach they have brought upon the local church. 

The Bible teaches we can repent of sins and ask God's forgiveness (Acts 8:22; 1 John 1:9). It also teaches that we can ask others to pray for us concerning our sins and transgressions (Acts 8:24; James 5:16).

When one sins in a public way, he needs to make things right with the church so if the matter is discussed among unbelievers at work or in the community it can be quickly squelched by members of the local church. 

This very thing has happened in our church and community recently, and I was able to stop the mouths of those who wanted to continue to stir the pot.