Just got into a discussion with my Sister, is there a limit to the amount of generations you can have?

I don't believe there's a limit. Unless - of course - you choose NOT to continue the family lineage.

Probably when everyone dies and no children to pass the house to? I'd imagine you'd need to restart...I strongly doubt they built in an option to bring back someone from the dead.

Illness gone uncured for too long can lead to premature death, no matter what the age. Then it's game over....