Hello nicoles01,
If I'm understanding you right, the Apple TV app is freezing when viewing TV episodes via your Roku streaming device. I can certainly understand how disruptive it could be to have your TV show interrupted while watching it. I'm happy to help you resolve this.
Here are some awesome troubleshooting steps for you to try first: If you can't stream or watch movies or TV shows from the Apple TV app, iTunes Store, or third-party apps. I also recommend updating your Roku device. You should be able to locate instructions on the Roku website regarding how to do this. This might be helpful: How do I update the software on my Roku® streaming device?. If the problem persists, follow the guidance in the "Still need help?" section of that first support article above.
Thanks for using Apple Support Communities.
Take care!