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Unbonded Fiber-reinforced Elastomeric Isolator (UFREI) as laminated elastomeric isolator is a relatively new approach to base-isolation devices with improved efficiency, cost-effectiveness, and ease. Base-isolated structures also become more susceptible to wind loads due to an increase in the period of the structure, and UFREIs have been found to be effective in mitigating occasional wind loads on isolated structures with the help of supplemental devices. This study investigates the multi-hazard response of the benchmark structures isolated using UFREIs under several hazards over a period of time. Hazard timelines consisting of probable prominent seismic and long-term wind events are generated for the analysis. Since fiber layers in UFREI are flexible in bending, the bond strength demand between elastomer and fiber layer decreases by a huge margin which delays any delamination failure. Thus, fatigue losses in the elastomer layers are used to characterize the damage induced in the UFREI due to multiple hazards throughout the timeline. Maximum principal strain in elastomer layers at various displacement amplitudes is calculated using finite element modeling, and it is further used to characterize the fatigue damage in elastomer layers. The final fatigue life of the designed UFREI is predicted using the obtained damage indices.