Although a Remainer, I do think we have to be careful here. The Quitters won a majority, and May followed their wishes by signing Article 50. Democracy was served. She then has consistently tried to get the best for Britain, and has worked hard at it in spite of all the back-stabbing from some of her self-seeking MPs.
So what question does a second referendum ask - the two obvious options are Quit on May's terms, or Remain.
Presumably most Remainers would continue to vote Remain (although I suspect some would change, given May's terms).
But what about the Quitters, a hard core of whom strongly disagree with May's terms. So how should they vote - presumably grit their teeth and vote Quit again. But in view of how much of the so-called "Project Fear" has already manifested itself as actuality, would some of the more moderate Quitters change their vote to Remain.
The outcome could be chaotic.
Whatever, this second attempt would rather make a mockery of Democracy. So I am strongly against a second referendum.