I've had the exact same issue. He shoots the first two powder carts, then on the third he won't. I 've made sure he reloaded is musket, I've tried restarting the memory. And still nothing. Have you figured it out yet???
Is this the chase sequence on a horse? I had trouble with this too. I ended up having to constantly tap the fire button over and over for him to finally shoot the darn barrel.
Edit: Someone else had the same problem it looks like. http://www.gamefaqs.com/boards/621796-assassins-creed-iii/64518538 --- If we don't study the mistakes of the future we're doomed to repeat them for the first time.