Use this:

• Help > Troubleshooting Information > Profile Directory: Open Containing Folder

A possible cause is a problem with the file places.sqlite that stores the bookmarks and the history.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.com/kb/Bookmarks+not+saved#w_places-database-file

Thanks cor-el. I have located the profile folder by going via Troubleshooting then show in Finder. Voilà: bookmarks and password data but only for the last day. so I need to find the equivalent folder in Time Machine to restore the bookmarks & passwords data, and that is not answered in either of those two links. On Time Machine, I get to home folder/Library/Application Support/Mozilla/extensions and there is just an empty folder. Again, there is no Firefox folder visible on Time Machine in Application Support no matter how far back I go.

Any further help would be gratefully received.

You can try to restore an older version of the file places.sqlite to get the bookmarks and history back.

There are 10 JSON backups in the bookmarkbackups folder, so you can also look at those and try to restore the bookmarks. The file size should be an indication how may bookmarks there are in it.

• http://kb.mozillazine.org/Backing_up_and_restoring_bookmarks_-_Firefox