Thermoplastic elastomers (TPEs) based on multiblock copolymers are an important class of engineering polymers. They are widely used in many applications where flexibility and durability are required and are seen as a sustainable (recyclable) alternative to thermoset rubbers. While their high-temperature mechanical behavior has received recent interest, few studies have explored their fracture and fatigue behavior. Understanding how the temperature and rate-dependence of the deformation behavior at both a local and global scale influences the fatigue resistance and failure behavior is critical when designing with these materials. In this study, the failure behavior in tensile, fracture, and fatigue of well-characterized, industrially relevant, model block copoly(ether-ester) based TPEEs were evaluated over a wide range of temperatures, deformation rates, and molecular weights. Small changes in temperature or rate are shown to result in a sharp transition between a highly deformable and notch resistant response, to a more brittle and strongly notch-sensitive response. This behavior surprisingly manifests itself as a threshold strain below which the cracks do not propagate in fatigue and increasing deformation rates decreases the materials toughness in fracture tests, whereas in tensile tests the opposite is observed. The change from homogenous to inhomogeneous stress fields for tensile and fracture experiments coupled with the viscoelasticity and strain-dependent morphology of TPEs explains why a different rate dependency is observed. Strain and stress delocalization is key to achieve high toughness. Digital Image Correlation is used to measure the size and time dependence of the process zone. Comparison with micromechanical models developed for soft, elastic, and tough double network gels highlights the dominance of high strain properties for toughness and explains the strong molecular weight dependence. However, to understand the rate dependence, the characteristic times for stress transfer from the crack tip and the time to nucleate failure must be compared. The results presented in this study demonstrate the complex effect of loading conditions on the intrinsic failure mechanisms of the TPE material, and provide a first attempt at rationalizing that behavior.