Brittle stars can, under optimal tank conditions, regenerate a lost limb, or a portion of one as long as the central disc in not damaged. However, if mobility is limited, they will have difficulty eating and in your case, may have gotten a bacterial infection.
This may sound creepy, but if you damaged a portion of one leg and it was all raggedy, you would have been wise to do a nice clean amputation, put some iodine on it(yes, iodine) and wait for regrowth, which is not fast under any circumstances.
I had a yellow angel who ate the tips off my poor brittle and they are just now starting to grow back. It has been months. (the angel went back to the LFS)
If you have a local marine biologist, I wou ld sugest contacting them to see if they can help your brittle star. My LFS also does fish/invert medical intervention for people. I have seen them spend $40 medication on a $3 fish! They are great guys!