Yes. You've been driving a little too fast and nothing bad happened? You might plead with the officer to ignore this minor misconduct. You're always a little sleepy in class because you study so hard until late at night? If you explained that to your teacher, he might not call your parents and give you a chance to improve your behaviour.
It would be more like "this one time": Can't you bend the rules, just this one time? – Können Sie nicht noch einmal ein Auge zu drücken? Or if you wanted to emphasise the character of exception: Können Sie nicht ein Auge zudrücken, nur dieses eine Mal? The latter being very close to my english suggestion.