XNA has officially been discontinued, with support no longer being offered by Microsoft. Does this mean that Monogame has died also? I see that the site still says it is based upon XNA 4. What is the official status of Monogame?
Quite the opposite. MonoGame stands to be the perfect replacement for existing XNA developers. It doesn't do everything that XNA did yet but there's no good reason why it can't. Coupled with the fact that it sports many more platforms and it's already being used in many reputable games I'm confident it will be great for some time to come.
Edit: I wrote this answer on my phone, let me elaborate a little more.
Firstly, MonoGame does not depend on XNA, it's an open source implementation of the XNA API and does not use Microsoft's implementation in any way. They make it clear in the Contributing to MonoGame instructions that no code from the XNA framework is actually used in the implementation, only the public API. Therefore, MonoGame exists on it's own without XNA.
Secondly, the MonoGame project is being actively developed. You can see on github there is plenty of commit activity going on. The most recent post on their website was 2 days ago announcing 2 MonoGame titles coming to PS4.
Third, the MonoGame forums are active. The most recent posts are today, and plenty of discussions going on around development, new game announcements, new platform support and solving problems. They also have other active social feeds like twitter and as Noctrine pointed out an "official status"
So, there's plenty of evidence to indicate that MonoGame has not died.