The effect of an added plasticizer on the change of electrical resistance under deformation at both stretch and compression is studied in polyisoprene composites containing dispersed nano-size conducting carbon particles at concentrations in the vicinity of the percolation threshold. A giant change of the electrical resistance (by more than 4 orders of magnitude) has been earlier observed at both stretch (tensoresistive effect) and compression (piezoresistive effect) of the composite containing 10 mass parts of carbon. The addition of plasticizer to the initial materials increases the strain sensitivity of the composite and broadens the carbon concentration interval of the percolation threshold. The observed improvements of the strain-resistance response are explained by two effects: 1) decrease of cohesion forces between carbon nanoparticles and 2) higher mobility of the carbon nanoparticles in the elastomer matrix in the presence of the plasticizer. The fatigue of tensoresistive effect as a result of cyclic tensile stresses was tested by means of a special home-made testing machine arranged with a LoggerProTM digital multi purpose data acquisition unit.