I guess your question can be partly answered by what is democracy? It means many things to many people.
It’s interesting that the majority of time in the representive democracy model we use most of the votes support very much the status quo with maybe a little bit of tinkering round the edge, it generally supports the economically, socially and academically priveledged as these are the people who, generally speaking are in a position to put themselves forward to represent us. Even if they aren’t at the start they are generally drawn into playing the game in order to survive in Westminster.
On the other hand when we have a one person one vote on an issue we actually get a snapshot of what people actually want, what their experience of life is, what their perceptions are on how this country is run.
This time it’s basically flown in the face of what the thoughts are of many of the people who usually act as the country’s voice, both in the political,economic and social fields.
What this whole Brexit vote has shown me is how unrepresentative our democracy is, the ruling elite who are supposed to represent us telling us what we think, why we made decisions and that we are wrong.
It’s this lack of understanding which I think forcing a second referendum on the people makes it undemocratic, it’s the ruling elite saying we don’t agree with what you think so try again.
If we have another vote it needs to be a different question, eg no deal or Mays deal.