Hello Phil Chappell.
If I understand your post correctly, your preferences are not saving in Mail or Notifications. I'd like to help.
Safe mode will tell us if the issue is related to a startup item or plugins, and sometimes corrects the issue. This article will tell you how: Use safe mode to isolate issues with your Mac
If everything is working correctly in safe mode, but is not working when you get back to your user account, please check the section titled "If an issue doesn't happen in safe mode" for the next troubleshooting steps.
If the issue continues while in safe mode, a test user will let us know if the issue is isolated to your account, or system wide: How to test an issue in another user account on your Mac. If the issue happens in the test user also, then please check the section titled "If an issue happens in more than one user account."
Let us know if that resolves this issue for you.
Thanks for using the Apple Support Communities. Take care.