How would you know if your vote would count for anything? If the people voted OUT and the government ignored it who's to say what other votes they will ignore.
This has been debated to death, 99% of politicians agree that the vote is cast, let's move on.
By this argument we'd only hold elections once, and move on.
A central aspect of a democracy is that people are allowed to change their mind, and that people are allowed to continue to campaign for a decision to be overturned.
So no, we won't move on. Even after a Brexit we won't move on - some of us will fight to rejoin, some of us will work for independence (for my part, I've offered to help one of the groups starting to work for independence for London).
But this is not over, even it if takes breaking the UK apart to finish it.
I suspect not; for one, I think many of the 4+ million who signed the petition for a new referendum would probably vote "Remain".