You have three or more possibilities to solve the Problem:
Use using
Whenever you are using a service do it inside a using block.
using (var serviceClient = new ServiceClient())
{
serviceClient.DoSomething();
}
Use the IDisposable interface (Controller implements it)
public override void Dispose()
{
_myServiceClient.Dispose();
}
Use Dependency Injection
Use dependency injection and a lifetime manager which makes the lifetime of the controller and service clients the same as the http-request.