Black star won't absorb the souls of some people

Solution 1:

From the elder scrolls wikia

"The Black Star is a re-usable black soul gem. As such, it is able to store black souls, which are always of the Grand level, along with white souls.
Like other soul gems, it can only hold one soul at a time. Unlike other soul gems, the Black Star is not destroyed after its contents are used - it is simply emptied and can be filled with another trapped soul. When trapping souls, any compatible soul gem in the inventory will be used before the Black Star."

Considering that you say you do get the animation, its most likely that another gem was filled instead of the black star.