How do I diagnose hanging applications?

I have a problem with an AIR application hanging. I'm publishing to AIR 3.7 for Desktop, running on Windows 7.

The problem doesn't occur very often, but when it happens, I don't get any error messages or warnings (I have set the AIR package to debug mode so standard flash errors appear). I simply get a Windows message saying the application has become unresponsive.

I've done the usual checking for memory leaks etc, but can't seem to find the cause.

Is there any way to diagnose a fault like this? Any logging program or something to tell me what's going on?

Thanks