How long does minor toothaches last ?

Depends: Depends on your definition of minor, your tolerance for pain, and the ultimate cause of the dental pain.

Depends on problem: That would depend on what is causing the problem in the first place. Toothaches are never normal, they are a sign that something else is going on. Recession, trauma, cavities, and infections can all cause tooth pain. If the problem persists for more than a couple days, please go see a dentist for an evaulation.