The phase behavior of a symmetric styrene - isoprene (SI) diblock copolymer in a styrene-selective solvent, diethylphthalate, was investigated by in situ small-angle X-ray scattering on isotropic and shear-oriented solutions and by rheology and birefringence. A remarkable new feature in this phase diagram is the coexistence of both body-centered cubic (bcc) and hexagonally close-packed (hep) sphere phases, in a region between close-packed spheres (cps) and hexagonally packed cylinders (hex) over the concentration range φ ≈ 0.33-0.45. By focusing on the transitions among these various ordered phases during heating and cooling cycles, we observed a strong hysteresis: supercooled cylinders persisted upon cooling. The stability of these supercooled cylinders is quite dependent on concentration, and for φ ≥ 0.40, the supercooled cylinders do not revert to spheres even after quiescent annealing for 1 month. The spontaneous formation of spheres due to the dissociation of cylinders is kinetically hindered in this case, and the system is apparently not amenable to any pretransitional fluctuations of cylinders prior to the cylinder-to-sphere transition. This contrasts with the case of cylinders transforming to spheres upon heating in the melt. The application of large amplitude shear to the supercooled cylinders is effective in restoring the equilibrium sphere phases.