The Talmudic Sages teach that the maximum that a very wicked person is punished in the afterlife in gehinom is 12 months. The public recitation of kaddish shields the departed soul from this punishment. Hence, kaddish is recited during the first year after a parent's passing.
However, the custom is to recite kaddish for 11 months only. Saying kaddish the entire 12 months would give the impression that the deceased was a very wicked person who needs protection the entire 12 months.
So, unless the parent specifically requested it, or unless it's known that the parent was a willful transgressor, kaddish is said for only 11 months.
Sources:
- Gesher HaChaim
- P'nei Baruch