I'm having a similar issue. I can not connect to an outside slingbox with my MacBook pro.
I get the following error:
Your Slingbox is unavailable. Streaming has been disabled.
Then I tried an old android phone that had the Sling App on it, and I was able to watch the remote TV with no issues.
I get the same error with Safari, Firefox and Google browsers. I am logged in to the sling site, and can see the right device in the dropdown.
MacBook Pro with OSX Mountain Lion.
Thank you for using the answers forums and that is a very good question. Being that you can connect on the Slingplayer and can not connect over the Slingbox web site I have a few articles I would like you to look over.
Hope this helps
Sling Moderation Team