In an email to Joystiq, a Microsoft representative said: "We are aware that Xbox v1 users are currently unable to access downloadable content via Xbox LIVE, both for the original console and Xbox Originals on Xbox 360. The team is actively working on resolving this issue so that the Xbox v1 community can continue downloading content until April 15."
No time frame was given for a fix to the disconnected servers, but it looks like Microsoft wants gamers to enjoy every element of the original Xbox's connected experience until April 15. Now we can all go back to ignoring these server shutdowns and stop acting like it's such a big deal. You know, because it's 2010.