Mixed content and expired session issues with SSL and wp-admin

You must check all the files you load within the admin pages (including files loaded from plugins); they should be loaded over HTTPS. WordPress takes care about the files it loads itself, but it doesn’t control if you or your plugins load resources over HTTP; you must fix it.

To find the resources loaded over HTTP you can use the Console log of Chrome or Firefox developer tools.

Also, there are some instances of wp-admin that loads resources from front-end. For example, the customizer is in the admin side but the preview is a iframe of the front end. If you have SSL only on admin, you can end up with troubles.

The best thing you can do is to use HTTPS in the entire site. It will be more stable, your users will love it and search engines will love it.