LYAPUNOV'S SECOND METHOD, ANYONE? Juan Non-Volokh cross-references two Brad DeLong posts on the Economics Nobel, one noting that awards recognize fields of study, the other taking the time to cite the award itself.
With respect to the first post, I recall some people in regional science suggesting that if public choice theory deserved a Nobel (James Buchanan), so did regional science (with Walter Isard as their candidate). Paul Krugman's recent professional work on suburbanization suggests there is still a discipline called regional science.
The open research question Vernon Smith's comment ("theory is incomplete, particularly in articulating convergence processes in time and in ignoring decision costs") addresses is one with lots of potential. Austrian economists like to discuss market process, but dislike mathematics. Convergence proofs are simpler with a lot of predetermined information.