Matthew 18:15-17 makes it pretty clear to me that the purpose of church discipline is to restore a fallen Christian who has been overtaken in some sin. We should go to them privately first, with humility, to show them their fault. If they do not repent, we should take two or three witnesses with us to again try to call them to repentance. If they do not repent, we should involve the church as a measure of last resort to call them to repent of their sin. If they don’t, we should withdraw fellowship from them and, as Jesus says, as a prospect for evangelism. They have demonstrated by their refusal to repent that they are not saved in the first place. Therefore, we don’t need to call them to repent of this particular sin but should call them to repent of their sins and trust in Christ as their Savior.
Matthew 18:15-17 does not say how long this process should take. I’ve only seen it happen in one church and it took several months to get to the stage where the church was called in to call the person to repent. I would say depending on the sin the amount of time might vary but I can’t imagine any place where the process would go on for more than 6 months.