I should have added that I have uninstalled and then reinstalled Firefox in the hope that this problem would be solved, but nothing was changed. As a result, I must fully log-in to every site that I visit EVERY time I visit, due to Firefox not remembering my history, as well as suffering many other problems as a result. This is maddening!

---Try Tools | Options | Security and set your preferences.

---"Security" tab contains Password settings.

---While in there set a Master Password for your browser.

---If I am mistaken, sorry about your frustration. I'll check back.

---Also, select the Privacy tab and select "Use custom settings for History". Adjusting settings as you wish, with some thought.

---While there; My suggestion would be to un-check "Accept Third-Party Cookies". Third-party cookies are the offensive ones and if a site doesn't allow you to log in without accepting them, then that site doesn't need to be allowed to surf the internet.

---Here's how mine's set. http://oi56.tinypic.com/2r712zb.jpg

Thank you AKA! I will try that.

UPDATE: Nope, that did not work!

What I find maddening and frustrating is that when I try to set the Tool/Options/Privacy setting to "Remember History", it will automatically revert to "Use Custom Settings for History" each and every time! What could be making it do this? (It will, however, keep any changes that I make under the "Use Custom Settings for History" option --- except for actually REMEMBERING my history!)

---That's interesting. "What could prevent me from altering/editing my browser settings (E.G., security/passwords and privacy/history)?" I'll have a peek around and see if anything has been discussed.

---Does it only happen with history?

Yes, AKA, it does appear to only be happening to my history --- bookmarks and other settings appear to be retained. Only my history, and log-in info/passwords for sites, are being deleted each and every time I log off or shut down my computer.

I should add that I have explored this topic at length within the questions previously asked in this forum, but could not find any similar problems reported by anyone else.

---You haven't recently downloaded/installed anything like the TOR Browser or TOR Package have you?

---With exception to having two versions of a plugin installed, I don't see anything that might be effecting your history. Try downloading the latest version of getplusplusadobe, removing getplusplusadobe16291 & getplusplusadobe16263 and installing the latest version. The only time more than one version of anything should be on your computer is when it is an update, SP or .Net.

---If you've tried everything you can think of, couldn't find anything in the forums or articles, then if you haven't, save your bookmarks to an HTML folder and uninstall FF getting rid of all user preferences. Then reinstall, and import only your bookmarks. Set the browser preferences however you chose now.

---You can install the Password Exporter plugin to collect and save your passwords so you don't have to remember the sites & passwords for future programming. After you install FF again, import bookmarks, set security & browsing preferences, then install the Password Exporter plugin, import passwords and uninstall the Password Exporter Plugin.

---When I uninstall, I use Revo Uninstaller (I use Revo Uninstaller Pro now) to uninstall and get rid of everything that came with the related program. After doing so, no reboot is necessary for anything.

moved

---Download and run Housecall, a stand-alone virus scanner... Just to ease your mind while trying to figure this out. It doesn't install, it's an executable stand-alone scanner.

http://housecall.trendmicro.com/

---Sorry about double/triple-posting. Got busy again with the `88 Mustang electrical and had to run. Moved second post down to here.

---There's a shortcut to "uninstalling FF, including user preferences" and that would be to close FF, delete the prefs.js file and restart firefox. All preferences for FF will be reset and FWIU all Thunderbird prefs as well. In windows XP it will be found in "root drive\Documents and Settings\Your account\Application Data\Mozilla\Firefox\Profiles\something.default\"

http://kb.mozillazine.org/Profile_folder

and/or

http://kb.mozillazine.org/Profile_folder_-_Firefox

---Did find a few more that had the same problem as you, when searching Google. Seems they're both on the new version 3.6.12 as well. Both around the 15th had a complaint/inquiry. No answer was given in either case, just the usual queue card posting of about:config BS that didn't relate.

AKA, I did everything you suggested, eventually including downloading RevoUninstallPro to remove EVERYTHING associated with Firefox, then downloading Firefox --- but still have the exact same problem! This time, it appears to be saving my history settings (i.e., "Remember History"), it just will not actually REMEMBER the history though! And now I have lost all my bookmarks in the process as well.

I have just wasted most of a day trying to solve this problem, including two different online chat sessions with Firefox support personnel, all to no avail. I am ready to take a sledgehammer to this damned computer already!

---If you did everything I suggested, you should still have your bookmarks saved (as an html file), all you need to do is import them once you get the problem resolved. I've done worse myself, when formatting and installing an OS and then realizing I forgot to move my bookmarks.html file to the temp drive... lol.

--- Sorry if my posts are long and contain many areas to consider/dwell, but that always seems to be the easiest & fastest way when dealing with anything tech, online. Messengers are faster but due to being a security weakness (they'll always be as long as the only "tunneling" firewall is owned by Symantec/Norton), and they never even get downloaded to my machines, so please, try to take in everything if you see it applies, and I will do my best not to steer you wrong by leaving something out.

---Open the tab you want to change in Tools | Options | etc. and then not only select your preference, but tic or untic a box for an "advanced/user choice". like untic "Accept Third-Party Cookies" and tic "remember search and form history". Also, untic "automatically start firefox in a private browsing session" if it's tic-ed... untic "clear history when firefox closes". Sorry if you have already, cause as you said originally, you've tried everything... but, if you don't change any settings (after changing the drop-down box for preferences) and click "apply", changes won't be saved.

https://support.mozilla.com/en-US/questions/763870

---I blame M$, IE and most of all Mozilla developers if the problem spreads to everyone who has IE8 on their systems. I don't have the issue, but my IE hasn't been updated from 7 when I upgraded and freshly installed Windows XP Pro SP3. If IE 7 is giving me grief with FF, I could only imagine what newer versions of IE could screw up for FF as long as they're allowed to fornicate behind the parents' (users') backs.

---Not necessarily related, but a healthy machine is a well-running one. I see an issue still, so it needs to be addressed and I'd suggest investigation be made as to how deeply the offense/mistake goes into your machine.

---It shows you have getplusplusadobe16263 installed where you had 

both getplusplusadobe16291 & getplusplusadobe16263 earlier. getplusplusadobe16291 is the newest version so you need to uninstall all versions and install the latest version. As said, in most cases, an update cannot run properly if previous versions are present & installed, you had both installed so as far as anyone can tell, both were corrupt.

---The only case where this does not apply is when in regards to .Net services (all versions are presently needed and are not backward compatible, meaning you cannot install .Net3.5 when .Net3.0 is not installed. Furthermore, If you look in Add/Remove Programs and you see similar instances, where Adobe Flash or Shockwave are installed, especially Java, and there's more than one format, the offender(s) need(s) to be uninstalled as well as the newest version and the latest version installed.