UPDATE 6/29/13 - New update has fixed this issue.
Last night I installed the new Windows 8.1 Preview and noticed the live stream wasn't working in the current version of Twit View (1.0.6) in the app store.
I was able to fix this issue and immediately submitted a new update to the Windows Store. It usually takes Microsoft around 5 days or so to approve an update and get it into the store, so you can expect to get the fix sometime next week.
Since the live stream is such an important part of the app, I will send anyone running the 8.1 preview an early copy of this update if they want to test it and get it sooner. Just email TwitViewRT@outlook.com, remember to tell us what kind of device/architecture you are using (either 32-bit, 64-bit, or ARM) so we can send you the right version of the update!
Warning - Installing the update before it gets approved by Microsoft requires you to unlock your system in order to sideload the app. Although this is a fairly easy and straightforward process that I can explain in the email, please note there are potential security issues in doing so.