I suppose that it's possible, that a reimage might help but I doubt it. Chances are, you got a bad card, if you've done eleven of these with the same image and everything has worked good except this one, then I would bet that it's the card. I assume you've tried the integrated wired network adapter and that is working? The fact that it seemed to have worked once on a reboot makes me think that it's installed properly but failing.
The only thing else I can think of is that you may have one mini that is only slightly differenet, maybe one off on the Rev# for the wireless card and the image is only slightly incompatible, not enough to show a driver error, but just enough to cause the issue you are experienceing. I guess the real proof would be to see if it worked, if you returned to the Windows 7 Starter factory install that it came with rather than hitting with the same image again and again.