I think Peter answers this correctly - at the end of the day the referendum question was pretty straightforward and there has been no suggestion of interference with the voting process itself.
There are problems with the referendum but its democratic legitimacy could only be questioned in terms of whether the electorate was fully representative and competent to make the decision. Many have suggested that 16 and 17 year-olds should have been allowed to vote as they have “more to gain (or lose)” than older people and, of course, many have suggested that ex-pats who have been out of the country for > 15 years should also have been included since many live in the EU and would potentially be affected.
I have sympathy for these views but, since the rules of eligibility to vote were in line with all other UK elections I think they are relatively weak. In particular those who have been living in the EU for > 15 years will generally have acquired the right to live in their host country and the right to apply for citizenship of that country so are less likely to be affected by the outcome.
There is also the issue that the 2017 election was fought with the Tories promising to deliver Brexit including repatriation of the legislative process, control over our trade deals and control of our borders - although May lost the Tory majority they are the largest party so that provides a separate mandate of sorts to carry Brexit through.
I say “of sorts” because if I hear the claim that 80% wanted Brexit because 80% voted for parties which promised to deliver Brexit one more time I shall scream. With only two parties in the UK who have any meaningful chance of forming a government and both of them pledged to take us out of the EU it is not as if Remainers had a choice. In fact even the Lib-Dems had watered their pledge down to holding a further referendum by the time of the election campaign.
As I see it the problems are a) that the vote was supposed to be advisory and b) that the manifesto which made promises as to the manner of leaving was undeliverable.
Point a) is an issue for those who seek (or sought) to overturn the vote - doing so does not rob parliament of the legal power to trigger article 50 so it would be a pyrrhic victory (this line of attack was abandoned anyway as far as I know).
Point b) is where many of the problems stem from and it is legitimate to ask whether people understood the implications of their leave vote - because in reality they were not just voting to leave the EU, they were voting to give the NHS £350 million a week, build more houses and schools, provide more jobs and keep all the benefits of EU membership yet allow the UK to free itself of EU influence and rules.
The “Leave means Leave” and “Willy of the People” crowd choose to ignore this and focus simply on what was asked on the ballot and, sadly, they are technically correct. It doesn’t stop me feeling that the public were conned
Many Leave campaigners promised control over immigration simultaneously with retaining access to the SM - it was always obvious that this was an either-or proposition but people accepted it as possible. That in itself might not have been a problem - politicians rarely have a problem reneging on manifesto promises and rarely (with the notable exception of the Lib-Dems recently) get called out on it. But the GFA kind-of crystallised the promises into something that had to be delivered. A border which was simultaneously open and closed.
Sadly I think that you are correct. As I said previously I think she won’t take it off the table because she thinks the EU will still blink first - I don’t think that will happen. While there is an irony that standing up for Ireland and insisting on a legally watertight agreement which ensures the open border (and let us not forget that it was our lack of integrity in the negotiations which forced the backstop upon us) means that the chance of us exiting with no deal and thus no agreement over the Irish border is that much higher I thinkthat the EU would rather be seen to have been united and failed than capitulate and fail to protect a member at the last minute.
, but I expect you’re only too well aware…could be worse, I expect 
