My guess is a memory leak. Can you monitor the memory usage of the Internet Explorer instance during the day via an application such as Process Explorer (http://technet.microsoft.com/en-us/sysinternals/bb896653.aspx)? If the application's memory use is (on average) increasing throughout the day, you are probably holding on to a reference to data that you shouldn't be.
It's difficult to offer specific advice regarding memory leaks without seeing the code though.
you probably have a memory issue with objects created and not gc'd. unfortunately, flash does not have good tools for building performance-conscience apps. the most helpful tools are in the system class but you'll need to read about flash and gc and go from there.
The Touchscreen TV is offsite however i will try and monitor it with that application you sent through.
I have just read that using event listeners may cause the problem.