Magneto-Rheological Elastomers (MREs) represent emerging composite materials consisting of small magnetic particles dispersed in a highly elastic polymeric matrix. Particles interactions with external fields (magnetic and electric) and external stresses result in a variation of rheological and physical properties of the material. In particular, MRE samples exhibit piezoresistivity, i.e. a change in the intrinsic material resistivity if subjected to an external stress. While literature reports experimental sessions aimed to establish the MREs piezoresistive characteristics and sensing capabilities, tests assessing the presences of hysteresis and cyclic drifts for multiple loading/unloading cycles of the MREs are not diffused. Nevertheless, these information are crucial to establish the quality and reliability of a sensing system. The presented work addresses the investigation of such parasitic phenomena for different MRE samples in order to assess their existence and relevance, to provide a more detailed and comprehensive description of the MRE piezoresistive effect as well as to enlighten further important elements useful to determine the possibility of using such materials for the realization of force or pressure sensors.