I think you're conflating various things all at once and, along the way, missing a few key points.
Firstly, most of the people in charge have indicated that the referendum result will be honoured and it's therefore almost certainly a question of when, not if, the UK leaves the EU. So that means that, for the moment at least, getting fussed about what many on the losing side a saying is a waste of effort. There is no second referendum coming.
But then again, to be pedantic, the question put to the British people was "Should the UK remain a member of the EU or leave the EU?". It follows that the result is advisory and it's now down to parliament to decide how best to go about implementing the decision. But if circumstances are such that it's clearly unwise to follow through with the decision, should Parliament be obliged to press on regardless?
This isn't a call for Parliament to ignore the result entirely, but merely to be sensible in implementing it.
On a second, scary point, Parliamentary democracy and direct democracy could well be about to collide hideously. Consider the following scenario: The Liberal Democrat party has taken the chance to pitch itself as the saviour of the UK's EU membership, directly appealing to the 16 million or so who voted to remain. In the (admittedly unlikely, but still possible) event where the Lib Dems won the support of these 16 million voters they would surely be the largest party and heading for a majority in Parliament. So, the question is, which democratic result wins? The referendum result, or the General Election won by a party standing on a "remain" platform?
This whole thing is a mess already, and could just get worse and worse. The sensible thing to do is surely to stick to the result of the referendum as far as is possible, but we shouldn't be too dogmatic about it either.