The effect of molecular properties on the rheological and fatigue behaviors of solid polystyrene (PS)/polyisoprene (PI) block copolymers was investigated. Linear model systems of PS-PI (SI), PS-PI-PS (SIS), and PI-PS-PI (ISI) block copolymers were synthesized via anionic polymerization with well-defined molecular structure variation such as block order, PI content, molecular weight, microstructure, and polydispersity. The different block sequences (SI vs SIS vs ISI) result, for similar PI contents, in different microdomain sizes, which correlate with the phase-separated morphologies as quantified via small-angle X-ray scattering (SAXS). The samples were mechanically characterized in the solid state via strain sweep tests to obtain their storage G'(gamma(0)) and loss G ''(gamma(0)) moduli at room temperature as well as their nonlinear properties determined via the Fourier transform (FT) of the stress response. The fatigue behavior was determined via strain-controlled oscillatory torsion tests. First, the effect of strain amplitude on the number of cycles to failure was analyzed via Wohler curves, specifically strain amplitude vs fatigue lifetime. A significant effect of the block sequence order, the microdomain size, and the chain dynamics on fatigue resistance was found. The fatigue resistance of SI diblock with 30 mol % PI outperforms the SIS or ISI triblock copolymer with a similar composition and, compared to neat PS, increases by a factor of 10 and even 4500, respectively. Second, the time-dependent stress response was analyzed via Fourier transform rheology to better quantify the time-dependent behavior of the nonlinear mechanical parameters and to determine quantitative parameters related to failure onset. Since the fatigue tests were performed under large amplitude oscillatory shear (LAOS), higher harmonics were detected and the time evolution was quantified in the FT spectra. Linear parameters such as the storage (G') and loss (G '') moduli, as well as the third (I-3) harmonic over the fundamental one (I-1), were analyzed, leading to clear indications related to both brittle or ductile failure mechanisms.