I suppose I should add that I'd accept that a series of referenda saying "Should the UK leave the EU?", "Are you sure?", "No, really, honest, are you really sure?", "Stop messing with me now, you don't want to leave do you?", etc, etc, while absolutely nothing happens to advance leaving in between times, *would* be undemocratic. But we voted to leave, and Parliament has enacted legislation to implement that, and the Government has set out to negotiate our exit as a result. So the scenario you are worrying about is categorically not what's on offer, nor would it be if Vince cable had his way.
As another point, he was returned to Parliament offering exactly this view, so he's representing his constituents and those who voted for the Lib Dems across the country. They happen to be in a significant minority, but still he is representing their views as is his democratic duty.
etc, etc. This is how democracy works; no argument is ever settled forever, nor should it be.