The Twitter Blog carries links to a number of blogs and discussions on the matter. My understanding is that the service is now running again, but while the official word is this was a ‘missing connection’ for shortcode users, the rest of the world isn’t convinced.
From the Twitter Blog
We've been tracking a missed connection between T-Mobile and Twitter for the past few days. If you're a T-Mobile customer using Twitter in the United States over our shortcode 40404, you may see intermittent failures (both with sending and receiving updates). We're working to resolve this issue as quickly as possible. Thank you for your patience!
Update (12/15 3p): We're still working on this and believe it to be a technical issue happening between T-Mobile and the folks who help run our text messaging. At this time we do not believe it to be a policy issue (as has been speculated). We're hoping for a resolution soon and will let you know when we know more.Update (12/15 4:30p): We've received word this issue has been resolved. We'll continue to watch closely and let you know if anything changes.