no, the electron affinity does not follow a regular trend as it is the energy chaange when one mole of electrons is added to 1 mole of atoms producing 1 mole of negatively charged ions.
As you are forming a bond (force of attraction between the positive atomic nucleus and an electron, proportinal to the magnitude of the charges and inversely proportional to [the square of] the distance between them) it is, in principle, always exothermic, but as can be seen from the data, there is hardly any benefit whatsoever from forming a negative magnesium ion (delta H = 0)
The location of the newly added electron clearly is implicated. With Na the electron can enter into the half filled 's' orbital but with Mg it has to go in the more diffuse 'p' orbital, which is farther from the nucleus on average.
Arriving at Al the increased nuclear charge makes the electron entering the 'py' orbital an exothermic process and even more so for Si with the electron able to go in the 'pz' orbital.
The next electron must enter an orbital that is already occupied with the electron repulsion that this entails, thus reducing the increase in electron affinity.
Next, for sulfur and chlorine you can see that the increased nuclear charge with a smaller radius is more important. And finally there is little advantage to adding an electron to Argon as it must go into the '3s' orbital, far away from the nucleus.