Google's John Mueller noted on Google+ that some webmasters may run into a hiccup when trying to use the download API for the Google Search Console CSV downloads.
John said the fix is to update the "App-Name" / "source" that you use to log in so that it matches the format specified over here.
That should then let you begin downloading the data again.
Google is coming out with a new Search Analytics API and John mentioned again that if you want into the beta, you should drop him a note on Google+ with your email address.
John said the beta should be coming out "soon."
We're working on moving this API to the existing set of APIs. If you're keen on giving that a spin, send me a note with your email address so that we can send you a NDA. I suspect we'll be able to get started with the beta soon, and in the meantime you can get familiar with the way the API works.
Forum discussion at Google+.
