I agree with Clement Atlee and Margaret Thatcher, referenda are “a device of dictators and demagogues”. The whole point of representative democracy is that we elect representatives to make decisions on our behalf. If we do not like their decisions, we can elect new representatives. Adding referenda into this mix creates conflicting mandates leading to the chaos we have now. Like everyone else, I have to accept the reality that the Conservatives made the mistake of offering a referendum and were elected. However, once you have made this mistake once, there is no reason why should not hold another referendum and so on, ad infinitum. But how soon you should reschedule another referendum is an important question. The democratically accepted answer depends on the result. Why does the result matter? Because of electoral churn. In the UK, there are over 750,000 new voters every year, and it is not democratic to deny them a say, especially if their views may have a significant impact on the result. So if the result of a referendum differs by less than 750,000 then you need to rehold the vote every year. If the result differs by less than 1.5 million, you need to rehold within two years, and so on.
On this basis, we should have rerun the EU referendum (leave majority 1.3 million) within two years.  If you do want to hold a ‘once in a lifetime’ referendum then you need to demand at least a two-third majority or more depending on how long you think a lifetime is. Unless, you are prepared to rehold the vote every few months, a simple binary choice majority referendum is a terrible idea.
 Peter Kellner estimates that Jan. 19, 2019 is cross-over day when remain attains a majority, assuming no-one changes their mind, and new voters follow the 2016 voting patterns.