Don't let the word 'senate' fool you, Rome was not a democracy. More can always be said, but there's an answer by u/Iguana_on_a_stick from our FAQ that explains the rough structure of the Roman Republic.

As for why medieval states didn't adopt democracy, it wasn't workable beyond the scale of a city-state. Imagine trying to hold an election in a country as large as France, but where nothing can move faster than a horse. Athens was a city-state. Rome's elections (however corruptible and undemocratic they actually were) only applied to citizens of the city of Rome. Autonomous cities in which elections were held to appoint officials or representatives were pretty common in the Middle Ages as a result of the Commune Movement, which I've written about here. But like the Roman Republic, many of these cities were far closer to an oligarchy than a recognisably modern democracy due to who could vote and how they voted, and how corruptible the system was. There was also the election of abbots and bishops, where the pool of voters was very small, but they were nevertheless elections. There was also Dithmarschen, written about here by u/Mikedash.

Recognisably modern democracy may not have existed in the Middle Ages, but neither did it exist in Rome. But the basic idea of elections never went away, and were commonplace in the Middle Ages.