I faced a situation when IISExpress stops after I stop my debugging session. Not always convenient especially if I want to tweak/adjust some html/javascript code.
The good news is that Visual Studio allows us to configure the behaviour.

I've figured out at least two ways to do that by unchecking "Edit And Contitue" feature:

1. Right click on your web project Properties->Web->Enable Edit And Continue 

2. Go to Tools->Options->Debugging->Edit And Continue