I'm going to add to this discussion because continuously reinstalling the 1Password add-on for Firefox is getting old.
Here is what's happening for me:
On my Macbook Air running Mac OS X (10.8.4) and using Firefox 21.0, I must reinstall the 1P add-on after restarting Firefox, which installs version 3.9.17 of the add-on. Everything else regarding 1Password works fine. (This was also happening with FF 20.0, so this problem is not new.)
Based on what I've read in this discussion, I can tell you that I have Firefox set to "Clear history when Firefox closes" and it specifically clears: Cookies, Active Logins, Cache, and Offline Website Data (just those four items).
Then the other significant thing is I have is an add-on called Session Manager, but I have no idea if this is having any effect.
Last, as much as I'd like to blame FF for their chronic release of full point distributions every few weeks, the remaining peculiarity is that none of the icons for any of my other add-ons ever go away. I think that's significant.
Does it happen in a fresh Firefox profile with no additional themes or extensions installed?