I am having the same problem you're having. It started when I upgraded to version 2.4.6 of the iPhone SlingPlayer app. My wife and I both have iPhone 4 hardware with iOS 5.0.1 and we're both having the same problem on our phones. Prior to 2.4.6, the SlingPlayer app was one of the most stable apps on our phones.
I've used the SlingPlayer apps on iOS for two years now; and since the 2.4.6 upgrade, we're lucky to be able to watch for more than 10 or 15 minutes without the app crashing entirely without giving an error at all or giving the error that you're getting about not being connected to the internet. You are not alone in experiencing this problem. I hope Sling gets it fixed quickly because the app is largely unusable on two of my family's iPhones.
I just seemed to solve my problems with the latest version (2.4.6) by reverting back to the previous version (2.3.3). I had a Time Machine backup that I was able to restore from. I hope you have a backup!! Follow the instructions here: http://gigaom.com/apple/recover-older-versions-of-iphone-apps-after-updating/. It took me less than five minutes, and my problems seem to have disappeared. If your problems only started happening after you did the last app update, I think you'll have similar results.
The only downside is that I won't be able to "Update All" on my phone for app updates until Sling releases a new version of their app that works; but it's a small price to pay to have my SlingPlayer sanity back again!