Rome was hardly a democracy when the Western Empire fell in the late 5th Century. Less than two centuries after the formation of the Empire, the Senate became essentially a defunct and impotent relic of the old Republic. "Senator of Rome" was a title for rich men who collected large sums of taxes to be paid to the Imperial treasury (and they often failed to do so), the Emperor essentially held most of the power, and gained more as time went on. Even though a new Senate was founded in Constantinople by Constantine in the 300s, it was really more a symbolic act than one of necessity. So, taking "the Fall of Rome" to be the "end of a democratic era" I would regard as fundamentally incorrect.

However, that being said, back to the original topic. This is a complex question because, first, even medieval states that declared themselves "Empires" or "Kingdoms" contained a fair amount of democratic elements - historically, it was the only easy way to appease the various ethnic groups within. For example, there is in fact a book that is going to be released next year by Anthony Kaldellis titled: "The Byzantine Republic" where he argues that Byzantium, despite being traditionally seen as a very strong autocratic state, based much of its strength on the motives and sentiments of the people. I very much look forward to reading that.

Anyways, to answer your question, the answer is "no". Most of the medieval Italian Maritime States were republics - the Serene Republics of Venice, Genoa, Pisa, Amalfi, Ragusa, Ancona etc. Most of these have their origins in the early medieval period (c. 8th and 9th Centuries), which already tells us that the democratic/republican spirit was not limited to ancient Rome and the Renaissance. This political system seems to have only directly worked for smaller states of the period, and especially those with significant trading wealth, hence, why these small Italian states were able to popularly govern without resorting to autocracy.