This question seems to answer itself. By definition, ‘the Middle Ages’ must have ended, or they wouldn’t be ‘the Middle Ages’ in the first place. No one thinks they are living in between two more sophisticated eras.
But notice the slippage here, from a period of time to a state of mind. While the Middle Ages extend from approximately the 6th century to the 16th CE, ‘the Middle Ages’ are a modern invention. It’s a paradox inherent in periodization, or the retrospective breaking up of history into chunks. Moving from the concept back to the time itself, you can ask a strange question that does not have a self-evident answer: Did the Middle Ages end?. . .