The logfile included only shows two recording sessions, no streaming at all. We need a log from when you were streaming and the disconnect happened.
This is going to be a network connection issue though. If you're on wifi, switch to a cabled connection. As you appear to be streaming to Twitch, grab R1ch's Twitch Test application and run that; it will give information on bandwidth to each server, as well as your connection quality to each (aggregate packet loss, minimum throughput choke, etc).
Even if your connection seems fine, streaming relies on constant minimum throughput stability. Something that browsing, watching streamed video, and most other general consumer uses do not reflect.