Part of the problem is that when the game has been off and the game catches up it decides that a certain number of babies have been born. Often these are all given the arbitrary age of six (and often all have the same mother!). That means that there are certain periods when a good proportion of the villagers are all the same age. I've seen this happen with a couple of my longer-lasting villages.

The answer, as so often in this game, is patience. Eventually the older villagers will start to die of old age and the younger villagers will be able to start having babies again. The only problem would be if your villagers were all aged in a narrow band that meant the youngest was aged over 50 by the time they started to die.