You mean they're trying to access a menu item that isn't accessible except if logged in, but their session has expired? In that case Joomla menu access check is what blocks access and attempts to send to the login page. CBs login page should be able to return them to that menu item after they login. If the menu item is public, but the endpoint isn't accessible unless logged in then it likely will not return them to where they were attempting to go as that's an access permission block and doesn't include the return URL. What CB page are they specifically trying to access while not logged in?

Public accessible content shouldn't be presenting a login screen. That would suggest there's an access check behind that content preventing the user from accessing it and requiring login. CB doesn't really have any control over this. Joomla does its menu access checks before the component does any of its endpoint access checks. If it's found the user doesn't have access to a menu item it sends them to the login page (we take over Joomlas login page in this case).

If the menu item is public, but the endpoint isn't accessible to public users then the endpoint will block access either by sending them to the home page or sending them to login; logging in in this case often will not return them to the page they were attempting to access, but this is entirely up to the component as they could send the return parameter in the URL to return them properly.

It sounds like for whatever reason your users think they should still have access to logged in content while not being logged in, which makes no sense from a security standpoint. Maybe just increase the session duration in Joomla global configuration so they won't be logged out so quickly.

Sounds like your menu module just isn't configured to display on every page. Either configure it to display on every page or use menu assignment like shown below to ensure it shows on your CB login page menu item, which if doesn't exist you will need to create.

docs.joomla.org/Help39:Extensions_Module_Manager_Menu#Menu_Assignment