This is a healthy server running SQL Server 2014 and Master Data Services.

And here it is a few months later, after trying to Explore a model.

The root cause of this is obvious here. This could be anything, or, it could be a missing max server memory config option set in the SQL Server database engine running on the same machine

However if you encounter the situation and need to verify that this is the root cause, you can do so by trying to load the WDSL definition web page http://localhost/MDS/service/Service.svc which will give you the following error:

Server Error in '/MDS' Application.

Memory gates checking failed because the free memory (45883392 bytes) is less than 5% of total memory.  As a result, the service will not be available for incoming requests.  To resolve this, either reduce the load on the machine or adjust the value of minFreeMemoryPercentageToActivateService on the serviceHostingEnvironment config element. 
  Description: An unhandled exception occurred during the execution of the current web request. Please review the stack trace for more information about the error and where it originated in the code. 

 Exception Details: System.InsufficientMemoryException: Memory gates checking failed because the free memory (45883392 bytes) is less than 5% of total memory.  As a result, the service will not be available for incoming requests.  To resolve this, either reduce the load on the machine or adjust the value of minFreeMemoryPercentageToActivateService on the serviceHostingEnvironment config element.

Source Error: 


 An unhandled exception was generated during the execution of the current web request. Information regarding the origin and location of the exception can be identified using the exception stack trace below.  

Stack Trace: 



[InsufficientMemoryException: Memory gates checking failed because the free memory (45883392 bytes) is less than 5% of total memory.  As a result, the service will not be available for incoming requests.  To resolve this, either reduce the load on the machine or adjust the value of minFreeMemoryPercentageToActivateService on the serviceHostingEnvironment config element.]
   System.ServiceModel.Activation.ServiceMemoryGates.Check(Int32 minFreeMemoryPercentage, Boolean throwOnLowMemory, UInt64& availableMemoryBytes) +108307
   System.ServiceModel.HostingManager.CheckMemoryCloseIdleServices(EventTraceActivity eventTraceActivity) +86
   System.ServiceModel.HostingManager.EnsureServiceAvailable(String normalizedVirtualPath, EventTraceActivity eventTraceActivity) +883

[ServiceActivationException: The service '/MDS/service/Service.svc' cannot be activated due to an exception during compilation.  The exception message is: Memory gates checking failed because the free memory (45883392 bytes) is less than 5% of total memory.  As a result, the service will not be available for incoming requests.  To resolve this, either reduce the load on the machine or adjust the value of minFreeMemoryPercentageToActivateService on the serviceHostingEnvironment config element..]
   System.Runtime.AsyncResult.End(IAsyncResult result) +624522
   System.ServiceModel.Activation.HostedHttpRequestAsyncResult.End(IAsyncResult result) +196075
   System.Web.AsyncEventExecutionStep.OnAsyncEventCompletion(IAsyncResult ar) +166

  


Version Information: Microsoft .NET Framework Version:4.0.30319; ASP.NET Version:4.0.30319.34209  

Alternately you can just check the Event Log, something which didn't occur to me but did occur to Tomas Lind, who put me on the right path.

I was able to reproduce this by exhausting available memory with a cool Sysinternals utility called TestLimit, which I learned about from a list of load testing utilities here.

testlimit64.exe -v 1 -c 1581

Definitely something cool to play with.