I want to apologize for the late reply. However, when it comes to the issue that you're having I think it is more of the iPhone settings. Whenever you pull up another application the streaming of the Slingbox will stop. I personally have an iPhone and it stops streaming video when I am watching YouTube, Slingbox and Netfix (just some examples) if I go into Facebook, or another application as well. You will have to reopen the application and start the Streaming again.
If you do have any further questions about multi tasking on your Apple device you should be able to contact Apple and they should be able to assist you with any further questions you have about this issue.
I hope this helps and have a wonderful day,
Sling media Moderation Team