By applying an excitation dependent, on-site restoring force to oscillators in a uniform one-dimensional chain with nearest neighbor coupling, this paper demonstrates the feasibility of reversible passive bandgap reconfiguration. Waveguide devices are most commonly tuned using active controls, component replacement, or by manually varying design parameters. Recent studies on wave propagation have pursued passive controls, where high amplitude environmental excitation triggers a potential well escape in an asymmetric, bi-stable system, automatically changing its linear spectra without user interaction. Current designs, however, do not return to their initial state upon later excitation amplitude reduction, instead requiring manual reset for continued operation. In order to allow fully autonomous function, a passively reconfigurable system must also be designed to return to its low amplitude state after environmental excitation amplitude decreases. This paper proposes a system in which reversible bifurcations are observed by introducing an excitation dependent on-site stiffness. Instead of a fixed, bi-stable potential energy curve, the oscillators have a single mono-stable curve at low energy levels and a different mono-stable curve with its own distinct linear spectrum at high energy levels. Numerical simulations are provided to demonstrate system transitions from propagation zone to attenuation zone behavior, and back, when subjected to increasing and decreasing excitation amplitudes.