That said, I don't think it's "undemocratic" to hold a second referendum. Parliament is clearly not on board with the whole idea, and the EU isn't really inclined to make a graceful transition. So let the voters make another statement, given what we now know.
If Brexit carries the day again, then Parliament will hopefully become a little more flexible, and the EU, for fear of alienating an important trading partner, will likely stop with the game of chicken as well.
And if Brexit loses then everyone can kiss and make up, with the new knowledge that actually pulling off an exit from the EU is harder technically and the full implications are more daunting than the voters anticipated.