Start Firefox in Safe Mode {web link} While you are in safe mode;

Type about:preferences#advanced<Enter> in the address bar.

Under Advanced, Select General. Look for and turn off Use Hardware Acceleration.

Poke around safe web sites. Are there any problems?

Start your Computer in safe mode with networking. Then start Firefox. Try Safe web sites. Is the problem still there?

Starting The Computer In Safe Mode;
Free Online Encyclopedia

Do a clean reinstall and delete the Firefox program folder before (re)installing a fresh copy of the current Firefox release.

• Download the Firefox installer and save the file to the desktop
  https://www.mozilla.org/en-US/firefox/all/

If possible uninstall your current Firefox version to cleanup the Windows registry and settings in security software.

• Do NOT remove "personal data" when you uninstall your current Firefox version, because this will remove all profile folders and you lose personal data like bookmarks and passwords including data in profiles created by other Firefox versions.

Remove the Firefox program folder before installing that newly downloaded copy of the Firefox installer.

• (32 bit Windows) "C:\Program Files\Mozilla Firefox\"
• (64 bit Windows) "C:\Program Files (x86)\Mozilla Firefox\"

• It is important to delete the Firefox program folder to remove all the files and make sure that there are no problems with files that were leftover after uninstalling.
• http://kb.mozillazine.org/Uninstalling_Firefox

Your bookmarks and other personal data are stored in the Firefox profile folder and won't be affected by an uninstall and (re)install, but make sure NOT to remove personal data when you uninstall Firefox as that will remove all Firefox profile folders and you lose your personal data.

If you keep having problems then also create a new profile.

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

• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Clean_reinstall

All the above suggestions were performed before I ask the question, however the issue persists! As I said there are no actual crashes!

Are you clearing any personal data when you close Firefox?

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": [X] "Clear history when Firefox closes" > Settings

You can check for issues caused by plugins and set all plugins to "Ask to Activate" on the "Firefox/Tools > Add-ons > Plugins" page.

Actually I'm using private browsing only, meaning that I've selected "Never remember history" and "Tell sites that I don't want to be tracked"

Besides the same plug-ins existed before Firefox latest update when the afore-mentioned issue didn't occur! OS is Win 8.1

UPDATE

I think the solution is closing Firefox with "Exit Firefox" button only, as the issue hasn't occurred again when I'm using this option.

However you can't do that when you have many windows open because it closes all of them.

Therefore I'd appreciate if any of Mozilla staff is reading this thread to try fix in any of the future updates!

Thanks!