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Of all of the Roman emperors before Marcus Aurelius, only Tiberius, Claudius, and Vespasian had sons. Tiberius' son predeceased his father and Claudius' son was murdered to ensure Nero's uncontested succession. Vespasian's children were born when Vespasian was still a general without even the faintest hint that he'd reach the purple one day and both Titus and Domitian grew up through their entire childhood as merely sons of a top general rather than sons of an Emperor.
People point out how exceptional it was that Marcus Aurelius broke a tradition of adopting heirs by passing the throne to his son, who was born while his father was emperor and raised as a crown prince. The question is, was this ever an intentional device? Surely Nerva was chosen as an emperor because of his status as an elderly childless man to serve as a stopgap, but beyond that one case? The only situation we have where an emperor could have passed the throne on to a son and chose not to was Claudius, and that was because his son was too young to inherit, and his son ended up paying for his father's decision to pass over him with his life.
This strange childlessness among sitting emperors is a pattern that ends up continuing. Septimius Severus, like Vespasian, had two sons already by the time he became Emperor, but no other Severan Emperor had a son.
I should point out that it wasn't through lack of effort by Augustus. Unfortunately he kept picking people who died before him:
After the sons of Agrippa died he was forced to go back to Tiberius who'd been pushed out of Rome to avoid overshadowing Lucius and Gaius.
Even being the emperor and having anything he wanted, early mortality could happen. I think this is something that could affect any elite household, I know there's at least one elite family that essentially gave up an adult son for adoption to another noble family simply to keep their name alive.