Let's assume it's my reputation at stake, not Christ's reputation...
The urge to protect one's reputation is a strong urge that usually reveals an insecurity. It's the sort of insecurity that believers who're truly resting in God's approval of them, in Christ, ought not to have. This urge to defend oneself usually reveals an underlying craving for man's approval. We ought not to be driven by such things.
However, it's not always kind to others to allow people to simply walk over you or say/believe falsehoods about you. There are good reasons why we often ought to stick up for ourselves. It confronts others about their sin, and it protects our reputations for the sake of ministry to others. The key word here is "others." We defend our reputation when it's in the best interests of others for us to do so. When it only soothes our own egos, we ought to feel no need for such defense. We get all the strokes we need from being in Christ.
This is easier said than done. It takes a strong confidence in Christ to have no interest in your own reputation for your own sake.
Yet we have seen it modeled well. Jesus defended himself sharply when it was necessary for confronting the Pharisees or establishing his authority to teach, yet managed to do it without a trace of self-interest. Paul also defended himself against his critics for the sake of his ministry to others, yet was hardly driven by a need for human approval. 2 Corinthians 10-12 is a great case study on this topic.
In short, we don't seek a "balance" between humility and reputation. Rather, we seek the good of others above ourselves and seek to rely only on God's favor for our approval. This results in both a deep humility and, at times, a vigorous response to slander. Both at once.
