It might be possible to lock out changes to your default search engine by creating a pair of files as described in this article: http://kb.mozillazine.org/Locking_preferences

In particular, I think you would need to lock these preferences:

• browser.search.defaultenginename
• browser.search.defaultenginename.US (for North America)

And as for the culprit, I can think of at least three possible reasons for this:

(1) An add-on is changing your default search engine at startup.

You can review your extensions for possible miscreants on the Add-ons page. Either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that stop the changes?

(2) An optional settings file named user.js is overriding your change at startup, or there is another problem with updating your preferences.

Please see this article for more information: How to fix preferences that won't save.

(3) A utility program like Advanced SystemCare is rolling back your changes between Firefox sessions.

In addition to ASC, some other security/utility software has a "home page protection" or "browser protection" feature that can do this.

Do any of those help?

If you do not keep changes after a restart or otherwise have problems with preferences, see:

• http://kb.mozillazine.org/Preferences_not_saved

Do a malware check with several malware scanning programs on the Windows computer. Please scan with all programs because each program detects different malware. All these programs have free versions.

Make sure that you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender:
  http://windows.microsoft.com/en-us/windows/using-defender
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked
• https://support.mozilla.org/kb/troubleshoot-firefox-issues-caused-malware

After you have sorted out the problem, use these add-ons;

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.