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.

FredMcDee Thank you for the response. You will see from my initial question, 1-3 of your response have already been tried. I do not think mal-ware is a cause as I have run full scans with three different apps to detect and none were found.

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

Jump around a few sites. Then check the history <Control><Shift> H. Close the browser, after a 10 count, open it normal. Is the problem still there?

If there is still a problem, Start your Computer in safe mode with networking. Then start Firefox. Do as instructed above. Then restart. Is the problem still there?

Starting The Computer In Safe Mode;
Free Online Encyclopedia

Create a new profile as a test to check if your current profile is causing the problem.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.

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

This is getting frustrating! None of the above appeared to make any difference. I have now:

1. uninstalled FF (ASC uninstall);
2. cleaned and defragged the registry;
3. saved and renamed the profile to another hdd (I wanted to later recover bookmarks and passwords);
4. searched system for all references to FF and Mozilla and deleted them (it seems that uninstall does not remove FF completely';
5. run three different anti-virus (nothing found);
6. emptied the Temp folders and Recycle bin;
7. Defragged the drive (in an attempt to overwrite deleted files).
8. Installed a fresh download.

It seems to be saving history between sessions on the same day (not yet checked for another day). One strange effect - although everything I could find was deleted and a completely new profile created, when I restarted (for a second time) it loaded all of the original Home pages set in the original profile. Where did it get that from?

I will now start reinstalling the addons, one at a time, to check if one of them is faulty (note: all the add-ons were taken from the Mozilla add-on page). This will obviously take several days as I want to check each for a day.

Cracked it! At last! I think. I have not made a positive negative check. After much in-installing and reinstalling of FF. (Why does standard un-install leave so many orphaned programme files/ folders/ registry entries? When I decide to un-install, Everything should be removed!!) Eventually I un-installed latest version of ASC. Even though all the options for "cleaning" and "monitoring" Firefox were turned off, it appears that it was ASC that was preventing the saving of history. Once that was removed then history started to be saved. This did not used to happen. I've used previous versions for many years with no problem but it seems that one of the recent updates (version unknown) started blocking FF history. (For obvious reasons, I will not re-install ASC just to prove the point. P.s for the moment, I am also staying with FF version 39

That was very good work. Well Done. Please contact their support and tell them.