Binary mixtures of granular media having differing diameters are combined in a horizontal cylinder and rotated like a drum mixer about its long axis. Within a few minutes of rotation at 15 rpm axial segregation occurs and the mixture separates into relatively pure alternating bands of the individual components along the axis of rotation. We describe an experimental system whereby the mixed state can be restored by changing the speed of rotation. The sensitivity of the reversible axial segregation effect to systematic variations of the glass bead diameter is reported. Measurements of the dynamic angle of repose of the mixed and segregated phases support an explanation for the reversible axial segregation effect involving the competition between axial drift and diffusion currents, leading to a diffusion equation with a negative effective diffusion coefficient.