I have both a live site, and a test site. Recently I upgraded to 4.6.9 from 4.6.7, and now I am unable to save any admin settings. None will stick--if I go to a different ACP page, or log out and log back into the ACP, the old settings are there. 

Strangely, both my sites are doing this now, and my test site does not use any caching at all. What could be causing this?

I think I solved the issue of not being able to save admin settings. I saw this error on the Data Storage page when trying to save anything:

• In order to enable this setting you must make the /path/to/task/task.php file executable (i.e. chmod 0777).

I have always had this chmod 0644 without issues, but after the upgrade something changed. Is 777 even secure?

Now I am able to save admin settings.

Yes. It has to be set to that in order to function correctly.

Just an update that 755 permissions also works, and is more secure.