The demand for building-integrated photovoltaics and portable energy systems based on flexible photovoltaic technology such as perovskite embedded with exceptional flexibility and a superior power-to-mass ratio is enormous. The photoactive layer, i.e., the perovskite thin film, as a critical component of flexible perovskite solar cells (F-PSCs), still faces long-term stability issues when deformation occurs due to encountering temperature changes that also affect intrinsic rigidity. This literature investigation summarizes the main factors responsible for the rapid destruction of F-PSCs. We focus on long-term mechanical stability of F-PSCs together with the recent research protocols for improving this performance. Furthermore, we specify the progress in F-PSCs concerning precise design strategies of the functional layer to enhance the flexural endurance of perovskite films, such as internal stress engineering, grain boundary modification, self-healing strategy, and crystallization regulation. The existing challenges of oxygen-moisture stability and advanced encapsulation technologies of F-PSCs are also discussed. As concluding remarks, we propose our viewpoints on the large-scale commercial application of F-PSCs.