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This is expected behavior, from what you describe, since you are essentially signing out of Tableau Server and then invalidating the same session authenticated for the embedded view.
You have a few options to change this which will depend on the experience you desire with the embedded Dashboard. If you have a core license, and Guest access enabled, then you can ensure permissions for the Dashboard allow Guest access.
Another method would be to use Trusted Authentication in the view, as described here: Trusted Authentication
All the above means is that a third-party cookie will keep a session validated for the Dashboard to be viewed.
Hope this helps!