I noticed that the Spotify App complains about not having an internet uplink, that happened several times during the last weeks. After quite a lot of debugging (firewall rules, reinstallation ...) I think I finally found the reason why: I have a "VirtualBox Host-Only Ethernet Adapter" on my system. Right after disabling this adapter Spotify is no longer in offline mode. On the contrary if I re-enable the adapter Spotify is not (immediately) offline again. Nevertheless I think this must be the reason.
Other software like the Firefox Browser does not seem to be affected by this, why does the Spotify App have these issues?