That's an interesting question, and I'm afraid it doesn't have a simple answer. The Earth's auroral ovals are present nearly all of the the time, even when the magnetosphere is geomagnetically quiet. During quiet times, the aurora appear as a very weak, diffuse glow. Spectacular auroral displays with ribbons of light that wiggle and swirl across the sky occur during something scientists call a "substorm." The length of a substorm and the auroral display depends upon how much solar wind energy has been stored in the Earth's magnetotail. During the growth phase of a substorm, solar wind energy is transported from the dayside magnetosphere and stored on the nightside in the magnetotail. The growth phase of an average substorm might last 1-2 hours. The expansion phase of a substorm starts when the energy stored in the magnetotail is explosively released. This is the phase when the most brilliant auroral displays occur, and it typically lasts about 30 minutes, although it can be longer. During the recovery phase, the aurora fade and the magnetosphere becomes quiet again. I'm not quite sure how long a typical recovery phase takes - sometimes this phase lasts only a few minutes, other times it is much longer. This entire cycle only takes 2-4 hours, so it can repeat several times a night.
Kris