We are aware of connectivity issues some users are experiencing when attempting to stream to Facebook using the SlingStudio console app's built-in Facebook destination option.
Facebook has acknowledged the bug involves a faulty application rate limit, that is affecting other apps as well, and they are working to resolve it (details: https://developers.facebook.com/support/bugs/347272016160276/
The issue is more likely to occur during "peak" times.
SlingStudio’s recommended workaround: Stream to Facebook using custom RTMP until the bug is fixed. Custom RTMP instructions : https://www.myslingstudio.com/Help/KB/KB-1148.aspx