The inability to save an edited email template is likely due to missing configurations or folder permissions.
I’m not entirely sure if I understood your issue correctly, but please note that you cannot save an edited email as a new template. If this is your problem, that could be the reason.
I hope this helps.
Are you using a wordpress in the same domain? Does this wordpress uses Wordfence or another firewall?
If not, do you have any kind of firewall enabled or some other web security?