Yup, we were playing it wrong! Hilarious! I laughed so hard when I confirmed it. I can clearly remember the question came up during our very first game. One of us asked our host,(also the owner of the game), if we shuffled our discard pile back into our draw pile once our draw pile had been depleted. His response was "I don't see why not." He was flipping through the rulebook at the time... We played almost all of the expansions before we figured it out. We will be starting over sometime soon, I hope.
Thanks everyone.