Only if the majority don't want Brexit (and all indicators are they don't) there is no problem and Democracy wins. You should be happy. As David Davies said "A democracey that does not let the people thing their mind is not a Democracy"
The only reason why Brexit mongs don't want a referendum on this mess is they know the majority of the UK no longer want Brexit. Otherwise they would be screaming for a referendum to prove their point and insist on Brexit. Which according to the Leave campain is the Single market and customs union (isn't that may's deadl?)
I also read that in the event of another referendum the biggest change would be the people that couldn't be arsed voting in the first pace that wished they did, which would be quite a small proportion of the electorate.
Also maybe the voters that have switched their opinion would probably cancel each other out, i'm saying that because an even number colleagues at work that have done exactly that.