If Firefox is set to run in permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History) then you may not be able to clear site data and you may have to exit PB mode temporarily.

• https://support.mozilla.org/en-US/kb/private-browsing-use-firefox-without-history
• https://support.mozilla.org/en-US/kb/common-myths-about-private-browsing

• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history"
• [ ] "Always use Private Browsing mode"

Thank you for the valuable info and links!

But my issue is only with clearing history in the History pull down. It recently stopped allowing me to Clear Recent History from that menu. If I Show All History I can then delete them manually.