Are you running the experiment using the Auto Current Range option? If auto current range is used points can be "lost" when the current range changes during the experiment.
You probably have a problem with one of the reference resistors. Autolab can be set to use a resistor within this range. I suggest you do some measurements on demi_cell and check which resistor is the problem. The problem is more with the hardware than with the system you are examining.
I have done linear polarization test to obtain corrosion current density and corrosion potentials of coatings.
I am examining the corrosion resistance of Ni-W-CeO2-Y2O3 and Co-W-CeO2-Y2O3 coatings (prepared by electrodeposition on Cu substrate) in NaCl (3.5%) solution.
I should mention that in a sample this jumping in current did not happened.
Also when I did corrosion test of copper substrate, this problem did not occurred.