I'm pretty sure the problem was murder, murder, murder, and more murder.

Many children died of illness back in ancient times, so poisoning them was a very effective means of ensuring the current emperor didn't have an heir, and there were so many poisons that just looked like a natural death from disease.

And not to mention a lot of their heirs by blood or adopted heirs were generals and which made "assassination on the field of battle" an option.

So yeah, both biological heirs tended to die en masse and even the adopted ones. Usually by the time the next emperor was selected, it was the emperor's fourth or fifth choice. Not the one they would have preferred.