Uhm, I wonder if facebook changed something. Can you enter the diagnostic panel and enable the logging to (at least) info level. Then try a signup with facebook and send to me the facebook-xxxxx.txt file you can find on wp-content/logs/newsletter folder.
There we should find the error.
BTW another user reported the same thing but when I try on my blog the signup it actually works.
If you can send me that file, we should be able to find the problem. If not I can update the module to be even more “verbose” while tracking the subscription steps.