@Stuart, you have misunderstood.
There may be a maximal element among the convex combinations of cyclic preferences, when the VM axioms fail to hold. SSB utility axioms have to hold in this case.
This maximal is a good candidate for choice from the cyclic preferences. So the claim that a violation of VM axioms leads to a money pump is false, even in the presence of cyclic preferences.
Read Fishburn’s Nonlinear Preference and Utility Theory (1988) or the very recent Essays in Honor of Fishburn, edited by S. Brams et al.
You should probably start your discussion from Merrill Flood’s 1952 article on preference cycles, available from Rand. http://www.rand.org/pubs/authors/f/flood_merrill_m.html
Page 42-44, Non Linear Preference, “The money-pump concept also reveals a narrow perspective on how choice might be based on preferences, and perhaps a lack of imagination in dealing with cyclic patterns. Although there is no transparent way to make a sensible choice from {p,q,r} when p>q>r>p, nothing prevents a person from considering preferences over the set of convex combinations of p, q, and r. And, if there is a combination in the set, then that persons has an ex ante maximally preferred alternative. As first shown in Kreweras (1961), this indeed can be the case, and we shall consider it later as part of the SSB theory.”
Here is a modern paper addressing some of these issues: http://hal.archives-ouvertes.fr/docs/00/08/43/90/PDF/B06008.pdf