Saving template changes produces error 404

Have you tried:

– deactivating all plugins to see if this resolves the problem? If this works, re-activate the plugins one by one until you find the problematic plugin(s).

– switching to the default theme to rule out any theme-specific problems?

– resetting the plugins folder by FTP or phpMyAdmin? Sometimes, an apparently inactive plugin can still cause problems.

– re-uploading the wp-admin and wp-includes folders from a fresh download of WordPress?

– increasing your available memory?