I am not a parent, but it is my belief that you never stop being a parent, once you are one. If you only had one child, and the child died, are you really no longer a parent? Similarly, do your brothers really quit being uncles, and your sisters quit being aunts?
Hard to say. When a child grows up and even dies before the parent, the parent would certainly still claim to be a parent. I suppose the same would be true for uncles.
If you go by the strictest of definitions, then a definition based on another person would no longer apply if that person dies, but that would be a callous thing to say. I would never be so pedantic to say, "Sorry, Bruce Wayne, but you're no longer a son since both your parents died." Mostly because I wouldn't want to get punched.
What bugs me is that there is no gender-neutral term for uncle/aunt. We have parents, children, siblings, grandparents, and great-grandparents, but a mixed group of parents' siblings would be uncles and aunts. A mixed group of siblings' children would be nephews and nieces. I did start referring to my sisters-in-law's children as niephces. I don't think it's going to catch on, though.
Also, why no gender-specific form of cousin?