History and cookies can be removed or not recorded several ways;

• 1) Running Firefox in Private Mode (nothing is recorded)
• 2) Privacy settings
  (Type about:preferences#privacy<enter> in the address bar.)
• 3) Many disk cleaners and anti-virus type programs can remove data from browsers. Open their settings and have them leave the browsers alone.
• 4) Mal-ware.

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.

Start Firefox in Safe Mode {web Link} by holding down the <Shift>
(Mac Options) key, and then starting Firefox. Is the problem still there?

You can check for problems with the places.sqlite database file (bookmarks, history) in the Firefox profile folder.

• Places Maintenance: https://addons.mozilla.org/firefox/addon/places-maintenance/

If the Places Maintenance extension can't repair the places.sqlite database file then remove all places.sqlite file(s) in the Firefox profile folder to make Firefox rebuild the places.sqlite database file from the most recent JSON backup in the bookmarkbackups folder.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.org/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file

Thanks - evidently updating to El Capitan turns off History. I turned it back on.

That was very good work. Well Done.