When you are viewing on your iPhone, are you using a wireless connection to a router or are you using the cellular service? Either way, you may need to check into what network speeds you are receiving. To check on your phone, you may need to download a free application from the App Store to check these speeds.
Below is an article that lists the minimum requirement for the network speeds.
Have you changed anything in the environment of the Slingbox? If the router, or modem was replaced you may need to factory reset the device the set it up for the new network settings.
Below is an article that describes how to reset the device, and a link that will take you through the setup process.
Sling Media Moderation Team