I figured out how to keep Skype 2.8 logged in and not prompt to 'Download Now' and quit.
I monitored ingoing and outgoing connections in nettop while Skype was logging in with the following command
$ nettop -m tcp
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A subdomain for 'skype.com' quickly showed a SynSent just before the 'Download Now' window appeared.
I added 'ui.skype.com' to /etc/hosts and flushed the dns cache.
$ sudo nano /etc/hosts
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$ dscacheutil -flushcache
Now Skype 2.8 should stay logged in!