This doesn't sound like a memory leak. What you're describing is a slow-down which is caused by putting too much work on the UI thread. Overall you should offload as much work as possible to a background thread or the compositor thread.
The app suddenly closes sounds like some unhandled exception, but it's hard to tell which one. You said the app works fine on WP7. Have you looked at known app compatability issues that occur once WP7 apps are upgraded to WP8? Check it out on MSDN @ http://msdn.microsoft.com/en-us/library/windowsphone/develop/jj206947(v=vs.105).aspx
This really isn't enough to go on. Is there something printed out in the output window once the app crashes? Can you tell what's the last managed method to be invoked before the app crashes? Can you try profiling the app for CPU and see what's the method that's most invoked? And profile for memory usage and see how's memory consumption right before the crash?