Thank you for contacting Slingbox Forum!
We are sorry that the Slingbox is not connecting properly after the router was turned off. You will need to reset your Slingbox.You will need to reset your Slingbox. Here is a link to assist you: How to reset your Slingbox to factory settings. It will, also, be necessary to go through the setup at setup.slingbox.com due to the fact that the Slingbox is not able to recognize that router after being off.
Hope this helps with your issue!
Have a great day!
Sling Moderation Team