In previous versions of visual studio (or some setting I set years ago) when i stopped debugging a web application the actual IIS express instance would keep on running. I r
One of the changes in VS2013 is to enable Edit and Continue by default in web application projects. When you have Edit and Continue enabled, the VS debugger attaches invasively to the web server process (e.g. IIS Express). When you stop the debugger, this kills the IIS Express process as well. If E&C is turned off, the debugger does not use an invasive attach, which lets the debugger stop without killing the attached process.
You can find this in your project properties on the Web tab, under the Debuggers section.