Double check to make sure your weapon has charges. If it's fully charged and not working, make sure it isn't by killing a simple wolf. Go to the Arcane Enchanter to make sure it's not an option (meaning it's already filled) for an enchant. Make sure to look under gems section. I haven't checked the Azura's Star due to getting the Black star. I'd wait to see if any other player that got Azura's Star to comment just in case.

I made the mistake of getting Azura's Star as well; it works, but only for lesser creatures. Wish I had made it into the Black Star instead, which accepts souls from people. The only thing I have to add about it's operation is to make sure that you don't have any empty soul gems in your inventory; your soul trap weapon, if fully charged, will fill the soul gems first before it fills Azura's Star.

i'd recomend filling azura's with giants or mammoths, if im not mistaken, they give you Grand souls every time you kill them (souls of giants are not Black even thou they are humanoids)

If you're positive that your Soultrap spell and/or enchantments work and that it's really Azura's Star, then it might be a bug.
Speaking of bugs, I've noticed that my Dark Star functions like an ordinary black soul gem and is still reusable. I'm not complaining, I'm just putting that out there.