Web error: "Mutex could not be created"

I’ve run across this a couple times and thought I’d document it here.

On occasion I get a server error for one of my websites “Mutex could not be created” with an exception System.InvalidOperationException: Mutex could not be created.

I’ve found the solution to this at ASP.NET forums in a response by Joao Morais.  It’s helped me out a couple times, but I’m still no closer to finding out what causes it.  (To be frank, it hasn’t happend enough to rise above the pain threshold where I need to track it down.)