We focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon, the resultant equations are essentially nonlinear. We establish the results using an analytical approach, including a variety of boundary conditions. We visualize the effective response of the designed sensor for several key components. It was obtained that the flexomagnetic effect is meaningful for less flexible boundary conditions. Besides, it was found that the failure originated from post-buckling occurs sooner if the numerical amounts of nonlocal parameter and the strain gradient one are respectively so small and exceedingly large.