Recent work on consistent Kaluza-Klein reductions on Einstein-Sasaki spaces prompted an intriguing conjecture that there might exist a consistent $S^5$ reduction of type IIB supergravity to give five-dimensional ${cal N}=8$ gauged supergravity couple
d to a massive supermultiplet that includes the breathing-mode scalar. Motivated by this, we investigate the possibility of augmenting the usual ${cal N}=8$ supergravity reduction to include a breathing-mode scalar, and we show that this is in fact inconsistent. The standard reduction to the massless ${cal N}=8$ supermultiplet depends for its consistency on a delicate interplay between properties of the ten-dimensional type IIB theory and properties of the Killing vectors on $S^5$. Our calculations show that turning on the breathing-mode is sufficient to destroy the balance, and hence render the reduction inconsistent.
