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We investigate the competition between granular mixing and segregation in a sphere rotating and rocking on two orthogonal axes. Operation corresponds to the continuous-flow regime and the flow within the sphere is three-dimensional and time-periodic. Experimental results are organized in a frequency/amplitude phase diagram showing modes of segregation (band formation/no axial bands); segregated bands are remarkably robust and survive rocking amplitudes as large as 60 degrees over a wide range of frequencies. Details differ, but the phenomenon occurs under both dry and slurry conditions, that is, when all air is replaced by a liquid. Experimental space-time plots of the stationary segregated patterns agree well with Poincaré maps obtained using a continuum model of the flow, suggesting that the final segregation patterns are relatively independent of materials tumbled.