Not sure about the answer to that. (Actually, have a possible answer further down). I haven't used the ux2 with video. I have used another computer to record video while I use another to record audio from the ux2 and then will later attempt to sync them up.
Is the sync problem happening from the start of the video or gradually as it progresses? I used to try different things to sync up audio and video (when using a normal soundcard) - can't remember what I ended up settling on. I used a a few variants of virtualdub and there were a few different ways they had that did things to match the audio up. I think some ways involved slightly slowing and speeding the audio to match, others took some frames out or added some extra ones etc. I don't recall there being a perfect way to do it though as the audio is always recorded at a different rate to video.
One possible solution might be to use pod farm, and put nothing but the digital delay effect on (in the "gear view") and set the mix level to 100%, feedback to 0, and the use the time knob to adjust how big the delay should be. This will then give only the delayed version of the audio and cut out the original audio. The time knob might not give the exact time you want and you might need to type the beats per minute into the bit on the right where it says BPM. The little symbol to the left of this (if there) needs to be turned off and the 'synch' light on the delay needs to be on. Press enter after typing in the bpm. This might take a while to get it right but a bit of testing might get it perfect.
If you don't know how to use pod farm, let me know and I'll let you know what things to do etc.
Also, if you are using pod farm, you would have to also go into pod farm's "Mixer view" and make sure that the output is set to send the 'effected' audio and not the original audio, to the video programme.