It's possible you have malware on your computer.

Please follow these directions:

• Troubleshoot Firefox issues caused by malware
• Refresh Firefox - reset add-ons and settings
• How to set the home page

If that doesn't help, please read How to fix preferences that won't save

After, use these;

Bookmark and use this; Mozilla Search Reset {web link} This add-on is very simple: on installation, it backs up and then resets your search preferences and home page to their default values, and then uninstalls itself. This affects the search bar, URL bar searches, and the home page.

Settings Guard for Firefox {web link} Detects and resets changes to settings that are frequently done by add-ons and application installers.

You can check the target line in the Firefox desktop shortcut (right-click: Properties) to make sure that nothing is appended after the path to the Firefox program.