The application ShutdownReason was "Configuration change", a more detailed message:
_shutDownMessage=Overwhelming Change Notification in c:\inetpub\wwwroot
Overwhelming Change Notification in C:\WINDOWS\Microsoft.NET\Framework\v2.0.50727\Config
This happened on Windows Server 2003, but not on XP.
The solution was to install the Microsoft .NET Framework 2.0 Service Pack 1. Now it is happy.