Nice chart there Baker
I thought it was at least no later than two weeks like Neil said, even one week sounds reasonable to me. It's been awhile since I've studies up on queens. So let's see... the queen is born with a little of her own pheromone, then when she gets mated her scent increases triple fold or more. So, if she doesn't get mated in a timely manner then after two weeks the queen pretty much smells like the rest of the bees, she can prob hang out with the rest of the colony, or they would do her in...But Why? there are no eggs left to make new queens.
I'll see what I can do to find a queen this time of year