I\'m using visual studio 2012 in the first days when I want to stop application in IDE, application was still running on IIS Express, I could browse and work with running ap
I recently faced a similar situation when suddenly my IIS Express stopped right after I stopped debugging. This happened after I turned on "Enable Edit and Continue". So if you disable this you will see that IIS Express stays running even after debugging is stopped.
Right click your project > click Properties > select the 'Web' tab on the left > uncheck the Enable Edit and Continue checkbox.