Well, you should bear in mind that despite being called "republics" that doesn't mean that these were what we usually understand a Republic is. For instance, in Spain, as late as the 17th century, Miguel de Cervantes uses the word "República" as a synonym of "the art of government", referring to the rule of the king of Spain, and that was just it's etymological definition.

When we talk about republics in the middle ages we are still talking about a oligarchy ruling a more or less defined territory, over which they have rights which are associated with the land and with a surname, implying it's an inherited right to rule. It may have some more limitations if you compare it to the most strong feudal systems, but, anyway, the rulers in a Republic sometimes even bear a nobiliary title.

People usually tend to think in some kind of binary terms, opposed to each other, as follows: Republic-Monarchy::More popular implication in the government-Authoritarianism::Plutochracy-Nobility. That's not how it works, however. The middle ages were a time of some kind of power formation and negotiation, closer to the idea of house societies than to that of the absolutism of the seventeenth century, and the bias we have towards the monarchy/nobility implying that those words meant authoritarian regimes as opposed to republics comes from the liberal movement in the early 19th century.

Medieval republics could indeed be more authoritarian than some monarchies. As I am Spanish I will show you the example of the Medicis in Florence (late middle age up to the sixteenth century) as opposed to the kingdoms of León and Aragón, both in Spain (Northwest and Northeast respectively).

The Republic of Florence was meant to be some kind of peoples-ruled regime, while, instead, was an oligarchy ruled by the guilds of the city, and, among them, by some notable families, which had enough money to finance their political career and used the institutions in their favour, so the ideal "democratic" Republic was more of an illusion. While the ruler of the city, the Gonfaloniere, was meant to be elected every two months through a lottery, in which the guild members would be included as contestants, these elections were rigged most of the times, and, finally, the Gonfaloniere title was enacted to be lifelong from 1498. Of course it was a title held by the Medicis. Also, of course, becoming a member of the guild was something only a really little part of the population could do: you had to had learnt the arts and crafts, and you had to have enough money so as to pay a quota, which kept it a luxury only a few families could enjoy.

Meanwhile, León and Aragón, both kingdoms of what today is Spain, had a situation more likely to respond to what many would imagine a Republic was, due to their particular history. From Wisigothic times, the king of Spain was elected, it was not an inherited title. While this ended when the Muslims invaded the peninsula, it shows how powerful many noble factions were within the kingdom. One of the first kingdoms which arose after the fall of the wisigothic kingdom was that of Asturias, which later became the kingdom of León, in the 10th century. Aragón, nevertheless, was just a marquee under the influence of Charlemagne, up until the 11th century, when it first became an independent marquee and, later on, a Kingdom. Both faced the same problem, a war against the Muslims and the need to repopulate the no man's land they recovered little by little during the conflict. This meant they had to make the conquered land interesting for their new inhabitants so that they were willing to defend it in case the Muslims tried to attack. That they earned it by giving "cartas pueblas", "fueros" or whatever: documents by which the new settlements earned some privileges and their inhabitants got some land for their crops to grow, along with communal lands (which still exist today) for their livestock and crops and some liberties like choosing the ruler of their territory (the church/a noble/the king) and the right to keep their own justice for some crimes (justicia pedánea, which kept the rulers from getting involved in every aspect of the peasantry's life). The chosen rulers had rights over big amounts of land, but not over all of it, and had the right to name the judges and even the priests in the territory, but their judges didn't have jurisdiction over some issues, and there were other judges, named by the king, which could contradict those, so that the peasants had some power, when United, to oppose to a feudal ruler. The Kings, of course, had to negotiate their power and influence with the nobles (it was the middle ages, and they were no absolute rulers), but they could diminish the nobility's influence and power by giving power to the peasants. This way, peasants had real influence in many territories in the north of Spain (this system was absolutely different from the 12th century on, but only from these territories to the south, due to the rhythm of the "reconquista").

Imagine: in the frontier of Castilla (a Kingdom arisen from León, on its East) and Aragón there was even a land, East of nowadays' Madrid, called Molina, which was a no man's land between the two kingdoms, and the ruler of that territory even became so powerful he ended up arranging the wedding of his daughter to the king of castilla. Also, Bilbao was the head of another territory, el Señorío de Bizcaya, whose peasantry had enough power to claim and keep their rights, different from those of the rest of Castilla, up to this day.

What I'm trying to point out is that a Republic didn't have to be more peasant-ruled, kingdoms weren't that much of a powerful institution, and nobility didn't have the same aspirations and self-awareness they developed in the 16th century. They may have overlooked their peers in the ruling of republics allegating they had a more important origin, but, for that time, they just weren't that interested in remarking those differences: they could even be more powerful than their own kings, to which they did bow. They became aware of the difference between old nobility roots ("nobleza de sangre", "blood nobility") and new nobility ("advenedizos", who bought their titles) when the king had reinforced his power so much he didn't need the troops the nobles could recruit ("mesnadas"), because he had his own professional army, much more powerful than theirs. They lost their influence, and became just captains of their own armies, while, a generation before they were OWNERS of those armies. That's when they start to worry about newcomers and so, to reassure their right to keep some power and influence, against those who bought it instead of inheriting it. But that happens right after the end of the middle ages