Hitting the "Find Updates" button in Firefox's Add-Ons box should get you LJlogin 2.1.2. For some people, it might. For others, it might not. For those who it doesn't work for, uninstalling the old and installing the new ought to work instead, but before you do, please look under Tools -> Error Console, see if there are any error messages that reference LJlogin, and if there are, post them here so I can maybe suss this out one of these days? Thanks.
Also, before I open up the floor to commentary, I am going to link to: The New Profile Dance. If you find that LJlogin Suddenly Stops Working For No Readily Apparent Reason, especially if you're on Windows, try this first.