Hey guys I experienced the same problem on my x10 not charging.
I first thought it was a battery problem because my x10 would turn on when I pluged in the charger, but then realized (after wiggling the wire) it was just the usb port that was loose, I have had 3 x10's with this exact same issue so it is most definitely a manufacturing issue.
But anyways after the third time it happened I decided to just deal with it, my solution was when you plug the charger in, gently pull the cord forward and slightly up it will start to charge, then just gently put the phone down, I usally lean it against something like a remote or side of the couch so it is pushing against the usb plug.
I've been using this method now for about 8 months
Sent from my Xperia X10a