The memristor is one of the modern microelectronics key devices. Due to the nanometer scale and complex processes physic, the development of memristor state study approaches faces limitations of classical methods to observe the processes. We propose a new approach to investigate the degradation of six Ni/Si3N4/p+Si-based memristors up to their failure. The basis of the proposed idea is the joint analysis of resistance change curves with the volt-ampere characteristics registered by the auxiliary signal. The paper considers the existence of stable switching regions of the high-resistance state and their interpretation as stable states in which the device evolves. The stable regions' volt-ampere characteristics were simulated using a compact mobility modification model and a first-presented target function to solve the optimization problem.