the avatars powers are part of him. if he had kids he would still be the अवतार becuase thats his bending ability-all of them. if he other benders can have kids and not lose their bending, the अवतार wont either.
In this image अवतार Roku's wife, Ta Min, is seen escaping from the eruption in episode forty six in a नाव with three people who could be their children. Roku never लॉस्ट his powers so I guess the अवतार can have kids.