Once you've won you are disqualified from entering. But up until then, you can enter as many times as you like until you "pro out" (see the thread "Proing out on the illustrator's side?" for clarification of what it means to pro out). You could be a finalist every time you enter and still not disqualify yourself.
And to be clear, keep entering a story in each quarter until you've heard that you won. You don't need to wait until the results are in from a given quarter to get your next entry in. They'll be happy to pull stories you entered before you knew you won from consideration, but if a quarter deadline passes and you haven't entered because you were waiting to hear, it's impossible to win in that quarter.