This website says that if one is saying Kaddish for someone who was not shomer Shabbos, one should continue to say Kaddish for 12 months instead of 11. What is the source for this practice?
The reason for the twelve months for someone who is not shomer shabbat is because the maximum time for a rasha is 12 months. That is, someone who deliberately refuses to keep shabbos or deliberately refuses to keep the halachos of kashrus would be considered a rasha in this sense. As we see Kaddish Eleven or Twelve Months
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.
Gesher HaChaim P'nei Baruch