I don't think there is an age limit for men, and it appears to be about 50 for the women. However, I have seen a few posts by players whose females have had babies when in their early 50s, but I think that is rare.

If your people die with no children then yes, unfortunately, your game will end. But never fear--keep your ear open for that tiny knock on your door by an abandoned child longing for you to take them in. Then you will have someone to pass your house on to.