Recently I encountered an issue in Firefox whilst attempting to login into my Twitter. Even though my login details were correct, I was not able to login. No error message, nothing. My first thought was Twitter was to blame, but it turns out it was my Firefox.
I also noticed on other sites this weird login issue was happening as well. When I would try and login to 99designs, I encountered a strange redirection loop.
The solution to fix your Firefox login woes:
Deleting your browser cookies is the easiest way to fix the login issues. You can delete specific cookies or you can delete them all. I opted for the second solution as it required the least effort.
I have no idea what caused the issue, but it seems cookies in my Firefox somehow corrupted. I did recently start using Firefox Sync, so it might have something to do with the problem. But I have no idea what the real cause was.
Hope this helps.