First, laptop or desktop? If it's a laptop, plugging in the second monitor may be making the GPU 'intelligently' switch over, which will break everything until you force everything over too.
Desktop, are both monitors plugged into one video card, or did you plug one into a motherboard video port (if so equipped)? The latter case isn't going to work. The former, well. Likewise, if you're using a USB monitor or USB monitor adapter, it likewise isn't going to work.
Please do post a complete logfile from a streaming attempt, it'll tell us a lot more about your setup and allow us to give advice and glean other information to suggest things. There's a stickied thread at the top of the forum, and when you open a new thread in here there's a reason it asks you to post a logfile if you're having an issue.