Unexpected ArgumentNullException when returning from a WCF operation call

I've recently run into a problem executing WCF calls to one of my services. I suspect that it has to do with a change to one of the Service Contracts, but I haven't been able to confirm this. I get the stack trace similar to the following:

System.ArgumentNullException:
   at System.Runtime.AsyncResult.End (System.ServiceModel.Internals, Version=4.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.ServiceModel.Channels.ServiceChannel+SendAsyncResult.End (System.ServiceModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.ServiceModel.Channels.ServiceChannel.EndCall (System.ServiceModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.ServiceModel.Channels.ServiceChannelProxy+TaskCreator+<>c__DisplayClass7_0`1.<CreateGenericTask>b__0 (System.ServiceModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Threading.Tasks.TaskFactory`1.FromAsyncCoreLogic (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at MyCompanyCanonical.Util.ServiceModelClient.ChannelFactoryExtensions+<UsingResultAsync>d__3`2.MoveNext (MyCompanyCanonical.Util.ServiceModelClient, Version=1.2.1716.1, Culture=neutral, PublicKeyToken=null)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at MyCompanyCanonical.Data.CostCodeRepository+<RelayCostCodesAsync>d__11.MoveNext (MyCompanyCanonical.Data, Version=1.2.1716.1, Culture=neutral, PublicKeyToken=null)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at MyCompanyCanonical.Service.Controllers.CostCodeController+<RelayCostCodesAsync>d__10.MoveNext (MyCompanyCanonical.Service, Version=1.2.1716.1, Culture=neutral, PublicKeyToken=null)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Threading.Tasks.TaskHelpersExtensions+<CastToObject>d__3`1.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Controllers.ApiControllerActionInvoker+<InvokeActionAsyncCore>d__0.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Filters.ActionFilterAttribute+<CallOnActionExecutedAsync>d__5.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Web.Http.Filters.ActionFilterAttribute+<CallOnActionExecutedAsync>d__5.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Filters.ActionFilterAttribute+<ExecuteActionFilterAsyncCore>d__0.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Controllers.ActionFilterResult+<ExecuteAsync>d__2.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Filters.AuthorizationFilterAttribute+<ExecuteAuthorizationFilterAsyncCore>d__2.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Filters.AuthorizationFilterAttribute+<ExecuteAuthorizationFilterAsyncCore>d__2.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification (mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089)
   at System.Web.Http.Controllers.ExceptionFilterResult+<ExecuteAsync>d__0.MoveNext (System.Web.Http, Version=5.2.2.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35)

The problem turned out to be the Microsoft.ApplicationInsights.Wcf package that I'm using (v0.27 at the time of this writing). There's a problem with the WcfDependencyTelemetryInitializer module that slowly builds up over time and then suddenly starts tanking your requests. This thing is a land mine.