After the passing of a parent, Heaven forbid, the child observes a twelve-month period of mourning, and thus, fundamentally, Kaddish should be recited for that entire period. However, the Rama (Rav Moshe Isserles, Poland, 1530-1572) brings (Y.D. 376) Poskim who ruled that the mourner should stop reciting Kaddish after eleven months. This is due to the Mishna's teaching in Masechet Eduyot (2:10) that the wicked are punished in Gehinam for twelve months. If a mourner recites Kaddish for a parent for twelve months, this might give the impression that he considers his parent a wicked person, Heaven forbid, such that the parent requires twelve months of Kaddish to be spared the punishments of Gehinam. Therefore, some Poskim rule that the child should recite Kaddish for only eleven months.
A second custom is mentioned by the Kenesset Ha'gedola (Rav Haim Benvenisti, Turkey, 1603-1673), who writes that he instructed people to stop reciting Kaddish one week before the culmination of the twelve-month mourning period.
By contrast, the Sha'ar Ha'kavanot (Rav Haim Vital, 1542-1620) cites the Arizal's teaching that a mourner should recite Kaddish for a parent throughout the year of mourning. The Arizal emphasized that Kaddish is recited even on Shabbat and Yom Tob, when the wicked receive a respite from the punishments of Gehinam. This demonstrates, the Arizal explained, that reciting Kaddish does more for the deceased parent than simple extricate the soul from Gehinam; it also elevates the soul to higher levels in Gan Eden. Publicly declaring G-d's greatness fulfills the Misva of Kiddush Hashem – glorifying the Name of G-d, which is the greatest Misva a person can perform. In fact, some Kabbalists teach that the Misva of Kiddush Hashem can rectify even the most grievous sins. The merit of the Kaddish recitation, then, brings immense benefits to the deceased parent's soul, beyond protecting the soul from the punishments of Gehinam. Therefore, the Arizal maintained that reciting Kaddish for the entire year of mourning does not necessarily give the indication that one considers his parent a wicked person.
Accordingly, the Hida (Rav Haim Yosef David Azulai, 1724-1806) writes that the custom in Italy, Egypt and Jerusalem was to recite Kaddish for twelve full months.
Nevertheless, the Hida recommended refraining from reciting Kaddish for one week. Similarly, the Ben Ish Hai (Rav Yosef Haim Baghdad, 1833-1909), in his Rav Pe'alim, writes that the custom in Baghdad was to conduct a memorial service (Arayat) after eleven months to signify that the deceased is not considered a sinner, after which the mourners would refrain from reciting Kaddish for one week, and then resume reciting Kaddish until the end of the twelfth month.
This is, indeed, the common practice in our community – to refrain from Kaddish for one week at the beginning of the twelfth month, and to then resume the Kaddish recitation until the end of the month.
It should be noted that this entire discussion applies only to the Kaddish recitations in the prayer service. The Kaddish recited after Torah learning or after the reading of Tehillim is recited by a mourner throughout the twelve months, even during the week when he abstains from Kaddish during the prayer service. Additionally, Hacham David Yosef, in Halacha Berura, cites his father, Hacham Ovadia, as ruling that if a mourner serves as Hazzan, then he recites all the Kaddishim included in the prayer service, even during the first week of the twelfth month.
Summary: Different customs exist as to when a mourner stops reciting Kaddish for a deceased parent. The generally accepted custom in our community is to stop reciting Kaddish during the first week of the twelfth month, and to then resume reciting Kaddish until the end of the month. Even during that week, the mourner recites Kaddish after Torah learning and Tehillim reading, and if he serves as Hazzan, then he recites all the Kaddishim that are part of the prayer service.