  We construct consistent Kaluza--Klein reductions of D=11 supergravity to four
dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At
the level of bosonic fields, we extend the known reduction, which leads to
minimal N=2 gauged supergravity, to also include a multiplet of massive fields,
containing the breathing mode of the Sasaki--Einstein space, and still
consistent with N=2 supersymmetry. In the context of flux compactifications,
the Sasaki--Einstein reductions are generalizations of type IIA SU(3)-structure
reductions which include both metric and form-field flux and lead to a massive
universal tensor multiplet. We carry out a similar analysis for an arbitrary
weak G_2 manifold leading to an N=1 supergravity with massive fields. The
straightforward extension of our results to the case of the seven-sphere would
imply that there is a four-dimensional Lagrangian with N=8 supersymmetry
containing both massless and massive spin two fields. We use our results to
construct solutions of M-theory with non-relativistic conformal symmetry.
