"Secure Connection Failed" error messages show up when a Firefox user tries to load a secure -- https:// -- website. The warning does not mean the website is malicious or insecure. Firewall and proxies behavior affects secure certificate connections. Sometimes the Internet connection fails to process a secure certificate and a user sees the warning pop up. Firefox allows users to bypass warnings and add exceptions to trusted websites. The exception saves permanently and the warning message will not generate for that website again.
Navigate to the websites that gives you the error in Firefox.
A Firefox warning window will pop up immediately.
Click on the "Add Exception" button at the bottom of the warning screen.
Click on the "Get Certificate" button next to the location text field.
Place a check mark next to "Permanently store this exception."
Click on the "Confirm Security Exception" button.
Click on the "Reload" or "Refresh" icon to refresh the Web page. The warning screen will be gone and you can browse the website.
Repeat the steps for any other website that generates the warning. This only happens on websites that start with "https://" because these are encrypted online websites, typically shopping and billing websites.