That sounds strange. Could you try to reinstall Firefox by downloading the installer again from mozilla.org? It shouldn't disable these features, but it might be that there is something weird going on with its settings.

Another thing to try is to start Firefox in Safe Mode (with add-ons disabled) in case there is an addon that overrides this preference. http://support.mozilla.org/en-US/kb/Safe+Mode

Do not use "Clear history when Firefox closes" to clear the "Browsing History".

• Tools > Options > Privacy: History: [X] Clear history when Firefox closes > Settings
• https://support.mozilla.org/kb/Clear+Recent+History

Clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, and passwords.

Make sure that you do not run Firefox in permanent Private Browsing mode.

• https://support.mozilla.org/kb/Private+Browsing

To see all History and Cookie settings, choose:

• Tools > Options > Privacy, choose the setting Firefox will: Use custom settings for history
• Deselect: [ ] "Always use private browsing mode"