It seems, this is not correct. I chatted with Discover and they say that for double cash back they count billing cycles, not calendar months. So, my 12th billing cycle ends on September 12, so after that day all I earn will be 1.5%.
Or, from your experience, they count calendar months?
I checked. My opening date was February 22, 2015 and my statements close on the 13th every month. So February 13, 2016 was the closing of my 12th statement and was the last date I see a doubling of my miles. So I was wrong and what Discover told you is correct. Sorry, my memory failed in answering your question. I should have looked back at my statements the first time I responded to your question.