There is a discussion going on between maintainers of the existing DI libraries, whether or not to build, maintain and support an adapter for the new ASP.NET built-in DI system. The Autofac maintainers have confirmed that they will create and support an adapter, while the Ninject team has been silent, and other teams such as the Simple Injector team (that includes me) have explained that they won't support an adapter.
Personally, I think that the ASP.NET Core built-in DI library is a nice and clean DI library, but it is limited to simple applications. As I explained here, many features that are required for developing maintainable applications built around the SOLID principles are not supported. However, just like the Unity DI library did a couple of years ago, I think that this built-in container might actually trigger developers to start using dependency injection, which is a win for our industry.
These limitations make the built-in container especially suited to configure and extend the ASP.NET system itself. To build large maintainable applications, you will need to use a different DI library. This of course is fine; you will have to pick the right tools for the job.
Unfortunately, up until now, the ASP.NET team has communicated publicly that using a different DI library, means you will have to write/use an adapter. This unfortunately is the wrong message IMO, because most DI libraries are incompatible with the API presented by the built-in container (as I explained here and here in detail). Only Autofac seems reasonably in sync, which explains why the Autofac team choose to maintain an adapter. But do note that even Autofac has proven to be incompatible with the abstraction that Microsoft defined, and they (just like StructureMap) had to make big changes to their product to even be able to comply with the abstraction. And the Autofac maintainers are severely frustrated about the whole process and the abstraction in general. And as I explained here, even the ASP.NET provided adapter implementation of Ninject is broken.
This message by the ASP.NET team to use an adapter is IMO a big error, because this stifles innovation (while the DI library itself doesn't; it's just another DI library). The ASP.NET team is promoting a model where both your application components and the ASP.NET system (and all other sub systems that will plugin in the future) will be registered in your custom container. It is much more reasonable and practical to keep your application configuration separate from the configuration of the ASP.NET system (as explained here).
Because of this, I find the use of an adapter for any container rather useless. As I shown here it is really easy to plugin your own DI container, while keeping it completely separate from ASP.NET's registrations. This means that you don't need support for Ninject to be able to effectively use Ninject on an ASP.NET Core project. The only thing Ninject needs to do is to create a version that is compatible with .NET Core (in case your product needs to run on that new platform).
UPDATE: "Ninject 3.3.0 was released September 26th 2017 and now targets .NET Standard 2.0 and thus also runs on .NET Core 2.0." source
So in a nutshell, I'm not sure that support 'is dying out', although some DI maintainers (such as the Simple Injector team, and probably Castle Windsor and Ninject as well) have chosen not to build, maintain and support an adapter implementation for ASP.NET Core, because it is not needed, and is only in the way.
UPDATE November 2016
I've been discussing some improvements to ASP.NET Core with Microsoft to make it easier to plugin a container that don't have an adapter (take a look at my example repository and especially to the Startup.cs of the Ninject sample project), but until now Microsoft seems to stall progress because (as Fowler states hisself) their "bias towards conforming containers [is] clouding [their] vision".