The lifespan of oceanic core complexes (OCCs) is finite and temporal variations in axial magmatism is often considered to be the main control. The mechanical weakening of an OCC's detachment fault and footwall is another potentially important process governing the formation of OCCs but has not received full consideration. \citet{Cannat_2009} suggested that the flexural rigidity of an OCC detachment's footwall would be very low during the formation of the OCC and significantly higher when the OCC formation terminates. They hypothesized that when gabbro intrusion occurs at an intermediate rate, weak hydrous minerals can form and coat the surfaces of gabbro bodies, effectively lowering the flexural rigidity of the footwall to a suitable value for the OCC formation. If the volume of gabbro intrusion becomes too high or too low, gabbro bodies construct a strong framework or hydrous minerals cannot form. Both ways, the flexural rigidity of the footwall increases, shutting off the OCC formation. We test this hypothesis using two-dimensional numerical models with temporal variations in the flexural rigidity of the footwall of an OCC detachment. Following previous modeling studies on the OCC formation, we construct numerical models using an open-source version of FLAC, a popular geodynamic modeling code. Brittle and ductile deformations are described by a strain-softening Mohr-Coulomb plasticity and a power-law rheology for dry diabase, respectively, and the transition between them occurs at 600\(^{\circ}\)C. Magmatic accretion in the brittle and ductile layers are assumed to occur at different rates that are prescribed functions of time. Magmatic accretion rates in the ductile layer (Md) represent gabbro intrusion rates. The effective flexural rigidity of the footwall is connected to Md through elastic moduli of the gabbro phase that are functions of Md in the depths affected by hydrothermal activities. In this presentation, we summarize results from preliminary 2D models and discuss whether time-variable flexural rigidity can really govern the life cycle of OCCs.