Suspensions of rods made up of a Zn(II) complex of a long-chain triester of meso-tetrakis[p-carboxy]-phenyl porphyrin (ZnP3) in saturated hydrocarbons have been characterized by rheological measurements. The anisotropy of isointensity contour plots of small-angle neutron scattering patterns characterize the orientation correlations in suspensions at rest and under shear. The highly thixotropic ZnP3 suspensions in cyclohexane exhibit weak yield stresses and are very shear sensitive due to fragile interactions between rod ends. Rheological and scattering data indicate that the relaxation of sheared suspensions can be described as a transition from a nematic-like distribution of rods to a random three-dimensional distribution. The related kinetics is a slow first-order process corresponding to the progressive disinclination of the rigid rods forming the segmented chains.