After doing a little bit of research on Cisco ASA routers, I see that they seem to use stronger firewalls than typical residential routers. You most likely will need to lower the firewall settings on the router when you attempt to setup the Slingbox. After you have the Slingbox connected to the network, I would assume you can turn those firewalls back up to your preference.
For further assistance with this, I would recommend contacting Cisco's Technical Support.
Hope this helps!
Sling Media Forum Moderation Team