Although the downtime must be frustrating for users and the temptation to build the shiny-new-system-that-will-solve-everything nearly irresistible for developers, I think they probably made the right decision not to do this. They have a runaway hit on their hands. That makes the risks associated with rewrite way higher (and they're already way high). One thing that people often do is start a "next-gen" project with an "architecture" team to figure out the new thing while a maintenance team (often lower-status within the organization) works on the existing product. This is so consistently bad an idea, it's pretty much a red flag all by itself. If I were ever going to rewrite a successful system I'd insist that it be the original team doing it.
I also wonder whether Twitter's downtime doesn't psychologically reinforce the sense that everybody's using it so it must be valuable. Scarcity and all that.
One thing about Twitter does make me pause. Haven't they hired tons of programmers? What are they all doing?