So if I understand the primary objection herein to a revote, it's that the democratic will of the voters must be observed. Therefore, if said voters want a revote to express their democratic will again, that's....bad? 
Sounds more like Brexiteer fanboys are afraid that their not good idea is now largely seen as not good, and if put to voters they will likewise pronounce it, not good.
Only a relatively small minority are hard-up decided against doing a revote. Voters are allowed to have buyer's remorse. It's why incumbents lose re-election. (Word is there are currently quite a few self-facepalming voters on this side of the Atlantic.)
And in this case, remember Brexit originally won with less than 52% of the vote! It's not like that razor-thin margin grants it an absolutely insoluble mandate for life.
Yes, the point about finality and not making the referendum a periodic recurrence is valid, but that's no reason to close up shop and ignore the will of the voters having serious second thoughts, any more than it would've been to ignore the original referendum results.
Not a Brexit fan myself, but how do you justify ignoring the results of a referendum?
If it's contradicted by the results of another, later referendum, surely the second referendum, carried on more recently and inevitably with more information, is more democratically valuable than the earlier referendum?
Plus, referendums are dumb anyway. The people shouldn't be voting on issues, they should be electing representatives to do that for them. Just because David Cameron decided to try to duck responsibility for EU membership by holding a referendum shouldn't mean Parliament isn't responsible for determining policy. If voters don't like Parliament, they can vote them out at the next election.
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