Hello all!
I too am having the terrible problem of getting my china tourist visa because my ARC card expires in September (2 months away). Ive tried a million things. First, I sent my passport home to a friend and we didn't know not to tell the consulate that I was not in the United States so they denied my request. IF YOU ARE SENDING YOUR PASSPORT AND APPLICATION HOME TO THE STATES DO NOT TELL THEM YOU ARE IN KOREA!
I found someone else going through the same problem on a forum and he told me that the consulate in Busan will grant you a visa even if your ARC card expires soon. I had my co-teacher call the Chinese Consulate in Busan and they confirmed that it will work... So Im keeping my fingers crossed. Good luck to everyone else with this problem! I hope this information helps!