FINALLY, someone has the same problem as me haha!!! I get the same problem and thought it was just for PC games. It ending up being a problem in console games as well. Every time a game was about to end and transition from game play to the menus the application would stop streaming and crash. I tried getting in touch with customer support through email and the response back to this question was with questions about the game,length,and the start or end of the game being played.
All I know is that at this moment the software is in a very buggy state and almost unusable for live streaming. It just sucks that this is one of the main features that was advertised for this product. I'd get in touch with their CS and let them you have the same problem except on PC that way they know it is not just the console or game that is causing the issue but, the actual software or hardware.