Thank you for using our online answers forum! I'm sorry to hear you cannot find a Slingbox in your Directory. Are you certain you are logged in to the correct account? You will need to be logged into the account the Slingbox was setup on. If you are logged into the right account, I would recommend uninstalling/reinstalling the application. You will not have to pay for it again as long as you are logged in to the same Google Play account you were logged in to when the application was purchased. Feel free to reply if there are any further issues.
Hope this helps!
The Sling Moderation Team