App tabs dissappear - sometimes on shutdown
I've pinned my app tabs, can shut down my browser session, re-start it and app tabs still appear. However, sometimes, if I shut down completely, when I restart Firefox, the app tabs disappear and I have to re-pin them.
App (pinned) tabs and Tab Groups (Panorama) are stored as part of the session data  in the file sessionstore.js  in the Firefox profile folder .
Make sure that you do not use "Clear Recent History" to clear the "Browsing History" when Firefox is closed because that prevails and prevents Firefox from opening tabs from the previous session.
-  http://kb.mozillazine.org/Session_Restore
-  http://kb.mozillazine.org/sessionstore.js
-  http://kb.mozillazine.org/Profile_folder_-_Firefox Firefox
It is also possible to use the "Show my windows and tabs from last time" setting, that is usually a more reliable way to restore session data.
- Firefox/Tools > Options > General > Startup: "When Firefox Starts": "Show my windows and tabs from last time"
Thanks. The link for showing Tools>Options was very helpful since I'm running Vista and the Menu bar was hidden.