Let me start this thought entry by saying I don't think Twitter itself will die in the sense that it will one day cease to exist as a web service or something. That's simply never going to happen. Actually, I think it will thrive as a user-friendly and universally adopted replacement to RSS and similar technolgies. What will dry up, however, are the instances of individuals who self-report in micro-thought format. The individual Tweeter.
For one thing, self-reporting to the web via Twitter or otherwise is a tedious and interruptive process that involves apparatus, no matter how portable, to affect. This isn't to say that we are not sufficiently driven enough to overcome this overhead today. These days we are all presently excited enough to have a relatively easy mechanism to report out to all our friends and strangers and to enjoy whatever utility comes from that. But the basis of this drive is merely the "fad" within a "non-fad" and any way you cut it, it's work. It's an expenditure of time and attention that people will eventually seek to reclaim and thus will equal fewer tweets about an afternoon spent cooking a meatloaf.
There are also the personal safety/security issues associated with detailed self-reporting that people are becoming more cognizant of. Tweets that let everyone know when your house is open for looting or that you're home alone were never a good idea, but in the excited adoption of a new power in communication, people easily dismissed or rationalized away the dangers. I believe that as time goes on and people realize, in particular, how searchable everyone's activities on Twitter actually are, these dangers will be heavier to accommodate.
When all is finally said and done Twitter's real user base will wind up consisting of those enterprises, profit-or-not, that find its format and reach most efficient for public outreach. Those entities that find RSS useful today will ultimately prefer Twitter for its more straightforward setup and organization. As I must often point out when typing such things, I also believe that exceptional individual self-reporters will also remain. These would be people like yours truly who find some sort of philosophical or egocentric purpose to the process of self-reporting and will likely never stop. Such people, however, will not sustain today's reputation of Twitter as a people's chirping chapel.