Not sure how I did it, but I wound up sending a story that had just been rejected the previous day back to the same magazine! I tried to email the editor and let him know, but apparently the emails and the submissions don't communicate very well with each other.
So, it got rejected again, only this time instead of the standard "I'm going to pass on this one" response, I got a more personal rejection. See below:
Thanks for submitting this story, but I'm going to pass on it. It's nicely written and I enjoyed reading it, but overall it didn't quite win me over, I'm afraid. Best of luck to you placing this one elsewhere, and thanks again for sending it my way. I look forward to seeing your next submission.
I have no analysis or anything, but it really makes me wonder what takes place on the "other side" sometimes.