Intermittent PolicyException: Execution permission cannot be acquired

We are intermittently seeing the following exception shortly after an App Pool recycle in an ASP.NET application:

System.Configuration.ConfigurationErrorsException: Could not load file or assembly 'Microsoft.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null' or one of its dependencies. Failed to grant permission to execute. (Exception from HRESULT: 0x80131418) ---> System.IO.FileLoadException: Could not load file or assembly 'Microsoft.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null' or one of its dependencies. Failed to grant permission to execute. (Exception from HRESULT: 0x80131418)
File name: 'Microsoft.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null' ---> System.Security.Policy.PolicyException: Execution permission cannot be acquired.
   at System.Security.SecurityManager.ResolvePolicy(Evidence evidence, PermissionSet reqdPset, PermissionSet optPset, PermissionSet denyPset, PermissionSet& denied, Boolean checkExecutionPermission)
   at System.Security.SecurityManager.ResolvePolicy(Evidence evidence, PermissionSet reqdPset, PermissionSet optPset, PermissionSet denyPset, PermissionSet& denied, Int32& securitySpecialFlags, Boolean checkExecutionPermission)
   at System.Reflection.Assembly._nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, Assembly locationHint, StackCrawlMark& stackMark, Boolean throwOnFileNotFound, Boolean forIntrospection)
   at System.Reflection.Assembly.InternalLoad(AssemblyName assemblyRef, Evidence assemblySecurity, StackCrawlMark& stackMark, Boolean forIntrospection)
   at System.Reflection.Assembly.InternalLoad(String assemblyString, Evidence assemblySecurity, StackCrawlMark& stackMark, Boolean forIntrospection)
   at System.Reflection.Assembly.Load(String assemblyString)
   at System.Web.Configuration.CompilationSection.LoadAssemblyHelper(String assemblyName, Boolean starDirective)

The specific DLL that fails to load varies from incident to incident, but is always one referenced by the main assembly.

We're running on ASP.NET 3.5 on Windows Server 2008. This seems to happen in batches affecting some but not all of sites on the same App Pool. We have a large number of sites all running the same code.

Once a site has failed to load a DLL it throws up a Yellow Screen of Death until the next App Pool recycle. We haven't been able to reproduce this behavior and the sites seem to work fine for days or weeks at a time (and many App Pool recycles) before failing.

Has anybody else seen similar behavior?

Update:

We've tried reproducing the failure by setting up a few hundred sites and writing a script to hit them repeatedly while recycling the App Pool once every couple of minutes and were unable to accomplish much other than loading down the server's CPU for a few days straight.

We then tried messing (locking one of the DLLs, changing the file permissions) with the copies of the DLLs that ASP.NET makes and managed to reproduce similar behavior but not the same exception.

Does anybody have any ideas on how to adjust the security policy to get it to throw a System.Security.Policy.PolicyException: Execution permission cannot be acquired. when loading a specific DLL?