Winky states in GoF that that her mother and grandmother served the Crouchs before her. In Grimmauld Place, the heads of the house elves on the wall all share the same nose as Kreacher, suggesting they are all his ancestors. And yet, we never see two house elves (a mother and father) serving a family, nor do we ever hear of any type of mating between elves. 

There are also instances of very old house elves (Kreacher and Hokey) who do not seem to have any children to continue serving the family's new generation. How are new elves born? Do they reproduce asexually without another elf?