I'll post this because I hate it when people find solutions but never post what theirs was. I had, as far as i am aware, the exact same problem. What I did was i closed the license manager window and went to the "update line 6 monkey". I logged in and it said it was having trouble connecting to my device. so i used the button on the left side of the menu to connect to my device. It was having troubles finding devices and suggested I unplug and re-plug in the USB for my device (which I did) and tried again. After it detected all my devices, it managed to find the UX2 and i simply "ok'd" the selection. after that i went back to the license manager and it was able to see and authorize my product. I've yet to confirm that everything works, but i did get the authorization to complete after having your issue.
