Thank you for contacting us Chris and I am sorry to hear about the problems with the 404 errors on your category pages.
I have run into a similar problem myself on some of my own WordPress websites and I believe I know where the problem is coming from.
I saw this problem when using the category and postname in the Permalinks combined with using a period in the Category base.
The reason that the Category pages are showing the 404 error with this configuration is because the WordPress routing system doesn’t know how to serve the category pages correctly since it thinks that they are static content, like Post and Pages, instead of being dynamic. The easiest way to fix this is to replace the period in the Category base field with anything else, or leave it blank and let the WordPress default setting take care of the rest.
I hope that this helps you get your Category pages working correctly and please let us know if there is anything else that we can do to help!