Are you sure you did everything exactly the same way both times? This recipe is very different from the one i make so i'm not familiar with it, but if you did it once and it came out then i imagine you inadvertently did something different the second time.
Was the dough thoroughly chilled?
Were the pans warm when you put the cookies in them?
Did you do them on a very hot day the second time?
Was the oven preheated to the same temperature?
I would think the temperature would be the thing that might have more easily changed from one time to another. What you describe sounds like how my cookies used to come out in rome where the flour is very different from all purpose. Could you have used a different flour (it calls for bread flour) the second time?