The last known execution took place in 43CE, as reported by Cassius Dio when one of the knights, who was charged with conspiracy against Claudius was thrown down the Tarpeian Rock.

Also at this time one of the knights, who was charged with having conspired against Claudius, was hurled down from the Capitoline by the tribunes and the consuls. (Cassius Dio, 60,18,4)

If there have been executions after this date we do not know. There are no sources mentioning executions by throwing someone down the Tarpeian Rock after that. At some point later in time, this method of execution has been prohibited by law. The Digest, one part of the Corpus Iuris Civilis, which has been compiled around 530CE, states, that

Non potest quis sic damnari, ut de saxo praecipitetur. (Digesta Iustitiani, 48,19,25)

which translates to: "No one can be sentenced to be thrown down from a rock.". When this law has been put in place originally, we do not know as well, since the Corpus Iuris Civilis is a collection of earlier roman laws, which, in some cases, date back as early as the first century BCE.