Note that is a New Private Window you do not use the disk cache and the cookie jar from a regular session (in PB mode a separate in-memory cookie jar is used). If it works in PB mode then it is possible that cache and/or cookies are corrupted.

It is more work to cleanup corrupted data.

You can reload web page(s) and bypass the cache to refresh possibly outdated or corrupted files.

• hold down the Shift key and left-click the Reload button
• press "Ctrl + F5" or press "Ctrl + Shift + R" (Windows,Linux)
• press "Command + Shift + R" (Mac)

Clear the cache and remove the Cookies from websites that cause problems via the "3-bar" Firefox menu button (Options/Preferences).

"Clear the cache:

• Options/Preferences -> Privacy & Security -> Cached Web Content: "Clear Now"

"Remove the Cookies" from websites that cause problems.

• Options/Preferences -> Privacy & Security -> "Use custom settings for history" -> cookies: "Show cookies"

For my main mozilla I used cor-el's solution of : You can remove all data stored in Firefox from a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History -> Show All History" or "View -> Sidebar -> History").

Using "Forget About This Site" will remove all data stored in Firefox from that domain like bookmarks and history and Cookies and passwords and cache and exceptions, so be cautious. If you have a password or other data from that domain that you do not want to lose then make sure to backup this data or make a note.