I have 2 lightning cables, and the new lightning to 30 pin adapter.
All seem to work in one way only (it's not reversable).
My guess is a software issue, since pins are assigned dynamically by the software, and the cables work, but only when plugged in the "right" way (though they should be reversable).
Was working for a few weeks, only noticed this starting yesterday.
I've tried restarting, both hard (holding home and power button), and a normal restart. This hasn't worked. I've also tried resetting all my settings, which also hasn't worked.
Seems to be a firmware issue, although it could be a problem with the cables, and I was unlucky on 3 different Lightning cables. That seems unlikely though. The port itself could be defective, but since it was working, and now it's not, I'm betting on software.