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I understand that reputation is far most important. One should do analysis and try to resolve the issue in a professional manner. I believe that every problem have a solution before its birth.
Its a very good question.The foremost thing you have to decide what is more important your job or reputation? I feel both but in case you have to decide one then Reputation is more important than job.
Considering to save your reputation, assess the problem and solve it with due diligence and diplomatically to save your reputation and job (may be one at risk). No gains without pains