No major advancement in integrated circuit design with highly-nonlinear resistance switching devices may be expected unless a robust theoretical framework, allowing to draw a comprehensive picture of the operating principles of these devices, is first developed. Recurring to nonlinear system theory, and, where necessary, developing novel methodologies for analysing the complex dynamics of resistive random access memories, is thus a fundamental preliminary step toward the subsequent development of a conscious and systematic approach to memristive circuit design. In this paper the Dynamic Route Map, a powerful system-theoretic analysis method for first-order nonlinear systems, is employed to uncover and explain the hidden mechanisms behind the emergence of memory loss effects in nonvolatile resistive random access memories fabricated at the Peter Grünberg Institut 7 (PGI-7) Forschungszentrum Jülich (FZJ) GmbH in Jülich.