They were all set to go. The world expected them to leave. They planned to regain independence. They wanted to make new laws. There were many who were opposed but it seemed to be the "will of the people". There were court challenges. No one was sure how it would all work out. Supporters of leaving said they would do new deals with various parts of the world. At first, it all seemed a dream but the world took notice when it had a referendum. The margin was tight but there was a momentum towards it happening. But eventually, it didn't go. It stayed where it was.
That was not the UK and the EU but Quebec and Canada. It is just possible that the UK might have a Montreal Moment and stay in the EU.
The shifting alliances and moving parts in the UK are moving towards the UK staying but the outcome is far from certain.
A second referendum might well mean that the UK people would vote to stay. However, the majority does not switch just because one has a second referendum. The polling and research in Ireland, which has had a "second referendum" on various issues (e.g. the EU as well as various social questions), demonstrates that there has to be a "change" either in the circumstances or public attitudes. For example, in the "second EU referendums" in Ireland, Ireland had secured concessions from the EU after the first referendum. Research shows that both those concessions, some "opposition remorse", and civic society mobilising were the differentiators. The UK might have to get concessions from the EU in this context if there is to be a swing. Moreover, the EU and its 27 remaining Member States have to be willing to concede something to the UK and offer something. This would require some patience on the part of the EU because many are now exasperated by the UK's indecision and approach over the last few years.
An extension under Article 50(3) might also lead to the UK deciding to stay. It is quite possible that the momentum involved in "leaving on 29 March 2019" may dissipate and there could be a swing towards the UK remaining. An extension is not a foregone conclusion and could be quite difficult to agree in Westminster and among the remaining 27 Member States. An extension that it is too short is meaningless but one that is too long could raise problems in the UK (among supporters of Brexit) and in the EU (e.g. would the UK participate in the European Parliament elections in May?).
It is more likely now that there will not be a No-Deal Brexit but it is certainly not over yet. The odds of an extension and even a second referendum are rising in this drama which will be the stuff of movies in years to come. The Oscars in ten years' time or so will have a movie or two dedicated to this drama.