Topological states of matter have attracted significant attention due to their intrinsic wave-guiding and localization capabilities robust against disorders and defects in electronic, photonic, and phononic systems. Despite the above topological features phononic crystals share with their electronic and photonic counterparts, finite-frequency topological states in phononic crystals may not always survive. In this work, we discuss the survivability of topological states in Su-Schrieffer-Heeger models with both local and non-local interactions with larger symmetry perturbation. Although such a discussion is still about ideal mass-spring models, the insights from this study set the expectations in continuum phononic crystals, which can further instruct the applications of phononic crystals for practical purposes.