Following the Torah reading on Monday and Thursday, it is customary for the Kaddish to be recited by somebody who is observing the year of mourning for a parent.
There is considerable controversy surrounding the question of asking the cantor to recite the Hashkaba prayer for a deceased parent beyond the year of mourning. Rav Yaakob Molcho (Jerusalem, 17th century) is cited as asserting that it is improper to make a Hashkaba except during the year of mourning and during the week of the Yahrtzeit. He explained that when the Hashkaba is made, the deceased's soul descends from the heavens, and it cannot return unless a charitable donation is made in the deceased's merit. It is therefore not to the deceased's benefit to recite the Hashkaba prayer outside the usual times.
However, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his Rav Pe'alim, disagreed. He writes that there is no source in the Kabbalistic works for such a notion, that the departed soul descends from the heaven as a result of the Hashkaba and then requires charity to return, and so there is no reason for concern. In fact, the Ben Ish Hai brings a passage from the writings of the Arizal that appears to contradict the theory advanced by Rav Yaakob Molcho.
Hacham Ovadia Yosef, his Hazon Ovadia – Abelut, accepts the Ben Ish Hai's position, and writes that it is proper to occasionally have the Hashkaba prayer recited in memory of a deceased parent, even after the first year, and not only on the Yahrtzeit. By contrast, Hacham Baruch Ben-Haim discouraged this practice. One should consult with his Rabbi for practical guidance.
Summary: Different opinions exist as to whether the Hashkaba prayer should be recited only during the first year after a parent's passing, and during the week of the Yahrtzeit, or if it is commendable to recite the Hashkaba occasionally even beyond the first year, and even when it is not the Yahrtzeit. One should consult with his Rabbi for guidance on this matter.