Our application is attempting to write a file to a UNC folder using an ASP.NET web service running under .NET 4.5, IIS 7.5, and Windows Server 2008 R2. Howeve
Reboot your 'mywebserver'.
Marvel at the now mysteriously functional ApplicationPoolIdentity.
Install MS HotFix KB2545850 and learn the details about this bug in KB2672809 which also shows the steps to reproduce and demonstrate this apparently random problem. Direct download link here.
Speculate why Microsoft has not managed to release a normal windows update for this in the 3 years since that hotfix was published. While people still continue running into it and pulling their hair out because of this obscure problem.
Learn about the other folks who have shared and enjoyed this gift from MS that still continues to keep on giving:
Your Windows 7 dev machine probably worked fine because it reboots more often than the server. Congrats on your very well written and thorough bug report. I rarely see that here.