This is as designed... if there is no user logged on, then by definition the "use logged on user" setting cannot work as there are no credentials that can be used.
You'll need to specify credentials for the UNC repository instead of using the logged-on user setting. If it's only for the servers you can create a server-only policy with this setting and assign that to the affected machines.
it's not possible to set a policy on a repository, only on managed machines.
otherwise i need to duplicate all my repositories, configure them to use the service-account and set them as repository list for a server-only policy, which is not a clean solution, because then i double the amount of repositories, which can even cause conflicts while updating them.
Sorry, I should have been clearer
You don't need to duplicate the repositories - instead, you can create a policy for the servers and add the UNC share as a local repository: this will allow you to specify credentials that the servers will use. (I would advise disabling the "real" repository in the same policy so that the servers don't try to connect with the wrong credentials.)
So for example say that your UNC repo is \\server\share and is called "UNC_repo" and is set to "use logged on user." You would create an agent policy where you would add a new UNC repo called "UNC_local", still pointing at \\server\share, but with different credentials specified. Then disable the UNC_repo repository in the policy, and assign this policy to the servers.