Herr Logan
Critical Bastard
There are a few reasons the Batman and his ilk are super-heroes and cops and soldiers don't qualify.
A "hero" is one who acts with heroic intent, whether conscious of his heroic intent or not. To be "super" is to be able to perform acts that most people in one's community cannot.
While many cops and many soldiers are heroes, you cannot assign the label "hero" to all of them. You can't prove they do what they do for love, money, power, or whatever else it gives them. Not only is there potentially personal gain to be had from such a job, but these people work for the government and ideally follow orders that do not necessarily come from their own beliefs and passions.
They are sanctioned to do what they do by the government that is charged with protecting the taxpayers. They aren't giving aid to the community, they are simply an official part of the machine.
Because of the tremendous number of police and military operatives in the world, and because the abilities they have are shared with so many of their peers, I have a hard time considering them "super." If they stand out in their group, that may be different, but the difference between an officer and a civilian does not constitute "super."
I don't consider the Punisher to be a super-hero. What he does, many real-life ex-military NRA-backing nut-cases who stay in shape can do. He may have the innocent in mind when killing his prey, but he's primarily driven by the hatred of criminals. He's an exterminator.
The Batman risks his life to save others. His "war on crime" is not a real war, unlike the Punisher's. The Batman takes prisoners and leaves no casualties. He lives by compassionate methods. He risks his life and his freedom, for he is not officially sanctioned to do what he does. Now that Commissioner Gordon is retired, he has no friendly arrangement with the police. He works by his own rules, under no authority, performing acts most athletes and law enforcement can't, and always acts as a hero. That's the definition, in my opinion.