We mentioned Tweetro recently when we interviewed developer house LazyWorm Apps who are also behind the Windows Phone app MetroTube. The Twitter client is meant for Windows 8 and runs quite well on RT devices like the Surface. Unfortunately, it has also stopped working.
That’s not the fault of the developers though but rather due to in part to two reasons (1) it’s very popular (as is the OS) and (2) Twitter has a 100K token cap. Long story short, Twitter implemented new changes to how their API is used for third-party apps and it's causing problems--if an app goes over that "token limit", they get shut down and stop working.