Two Problems: IIS 6 Loses Impersonation Information and Cannot Read File

Split off from http://forums.asp.net/t/1384703.aspx/2/10?Two+Problems+IIS+6+Loses+Impersonation+Information+and+Cannot+Read+File
We're seeing something similar in a slightly different environment.  Our problem is with a web service (a vanilla Microsoft SOAP web service) and its client.
The web service has <identity impersonate="true" /> in the system.web section of Web.config.  Integrated Authentication is turned on.
I've started logging Thread.CurrentPrincipal.Identity.Name & .IsAuthenticated and WindowsIdentity.GetCurrent(false).Name, .IsAuthenticated and .AuthenticationType on the server side.
IsAuthenticated is always true for both identities.  Thread.CurrentPrincipal always has the right name.  WindowsIdentity.GetCurrent(false) does n ...