So I have a system of three electrodes, anode, cathode and reference electrode. When I apply a negative current and then register somehow the activity of the sodium chloride solution. Then I apply a positive current (same value) , so basically the flow of charges is inversed but I detect a much lower activity. Is it possible that the mobility of the ions varies depending of the sign of the applied electricity?
In a word, yes. What you're doing is called sodium chloride electrolysis. A diagram of the experiment is shown below:
Basically, because the salt has been heated until it melts, the sodium ions flow toward the negative electrode and the chlorine ions flow toward the positive electrode. So, since you are turning on one at a time, and your solution is not an equal solution, you would detect more activity at one time than another. Another thing to keep in mind for this experiment is the electrodes would need to be the proper materials, polarity, etc. for this to happen.
WARNING! This experiment produces chlorine gas, which is deadly. Please, do not attempt this without proper equipment, a proper workspace, or proper instruction. Doing it without any of these three, or even with all three of these, can end up badly.
I hope this helps!