A natural demographic shift has taken place. By January 2019, even if nobody changes their mind, the country will be pro-Remain.
By January 2019, even if nobody changed their mind and everyone voted the same way as they did in 2016, the natural demographic shift of the UK would naturally mean that a second referendum would return a remain vote. 
Given that older demographics overwhelmingly voted to leave the EU, and younger demographic largely voter to remain, the mathematics behind the nation's demographic shift dictates that in January, Britain would no longer be a pro-Brexit country, even if nobody changed their vote. The mortality rate in Britain shows that the oldest demographic in the UK is dying off at a rate that cuases the number of Leave voters to shrink by 1,350 per day. Combine this with the two million voters that have reached 18, the legal voting age in the UK, since the 2016 referendum, and by January 2019, statistically, the UK will be a pro-EU nation.
Our democracy relies on the results of a nationwide vote, administered at a specific moment in time. Even if the demographic changes hours later, it is not practical or reasonable to expect that we should override the outcome of the vote because of a demographic shift. The outcome of the vote was final. It must be respected. Otherwise, how often do we have to have nationwide elections? Every year, to account for shifting demographics? Every six months? Whenever there is a significant demographic change? This is not practical.
The oldest demographic voted to Leave the EU by around 2 votes to 1. Among young people turning 18, 87% support Remain. Given the rate old people are dying, and the rate young people are turning 18, mathematically, the UK will be a pro-Remain nation by January 2019.
The demographic shift is irrelevant. The referendum accurately captured the will of the people in 2016. It was, therefore, legitimate. Therefore, the results must be respected.