Biology involves inherently complex three-dimensional designs. In addition to the geometric complexity, thin and complex biostructures composed of membranes such as insects, wings, and plants leaves can achieve complex functionalities under vibrations, such as maneuverability and resistance to strong winds, respectively. They do so by changing the shape and curvature of their membranes and ribbons. Achieving such capabilities in advanced materials would have important implications for a wide range of applications, such as threedimensional (3D) microelectromechanical systems (MEMS), sensors, and energy harvesting devices. Such applications experience cyclic deformation up to 20-30% length compression during operation. To this end, this paper investigates mechanical cycling of a number of microscale 3D polymer-based kirigami architectures. The mechanical response of these structures revealed stable and resilient behavior equivalent to flexible natural systems upon cyclic compression up to 50% of their initial height. To understand crack formation and growth, in situ scanning electron microscopy (SEM) under extreme compression of 100% of their initial heights reveal internal stresses and permanent change in the curvature of the structures, resulting in the formation of cracks after 100 cycles. To enhance their fracture toughness, computational modeling, as an optimization tool is used to provide guidelines to eliminate crack growth.