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Technologos comments on Money pumping: the axiomatic approach - Less Wrong
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I'm very busy at the moment, but the short version is that one of my good candidates for a utility component function, c, has, c(A) < c(B) < c(pA + (1-p)B) for a subset of possible outcomes A and B, and choices of p.
This is only a piece of the puzzle, but if continuity in the von Neumann-Morgenstern sense falls out of it, I'll be surprised. Some other bounds are possible I suspect.
Perhaps I'm confused, but I thought that the inequality you described simply refers to a utility function with convex preferences (i.e. diminishing returns).
I agree in general that discontinuity does not by itself entail the ability to be money-pumped--this should be trivially true from utility functions over strictly complementary goods.