I don’t know if this is a general issue or not but Visual Studio 2013 closes automatically the IIS express instance the same time I press the “Stop Debugging” button.

This is very annoying to me because usually I don’t start IIS Express server just for debugging but also for small CSS or HTML changes.

Anyway, you can disable this behavior by going in Visual Studio -> Tools -> Options -> Debugging -> Edit and Continue and uncheck the “Enable Edit and Continue” checkbox