What I'm getting from your post is that you're losing the the connection to the Slingbox from time to time.
In this case and before you receive any response from the forum users, you can provide more information or background of the issue.
For example, you can provide information about the network layout or error messages when the Slingbox gets disconnected.
Also, make sure that the Slingbox is connected to the wall outlet and not using a power strip and hardwired to the main router.
Besides that, you can discard a Dynamic IP affecting the Slingbox connectivity.