There isn't a limit to the amount of generations in a family if you have version 1.00.09. If you have any of the versions before that one, there is a bug that will effectively end your family at 30 generations.

However, if you would like to upgrade your game (to 1.00.09), read the post here carefully.

To check to see what version you have, open the game, go to the Menu, and look in the lower left hand corner. You'll see something similar to '1.00.09 LDW' there.