Before the referendum, Brexits thought they would lose by a small amount. They set up a petition to repeat the referendum until their was a 60/40 majority in either direction.
Which seems quite sensible and legitimate to me. It doesn't matter which way the vote goes only that there is a substantial majority in favour one way or the other. Until then it's not settled. And it's never settled for eternity - It's an inalienable right to change one's mind, take into account changes, new information and evidence.
It's how democracy works. We keep voting for governments and representatives, and when we find one which suits the majority they keep getting re-elected. When things change we vote for someone else.
There is nothing wrong with keeping on voting to come to a consensus. It is how it has always been. It's only hypocritical brexiteers having claimed victory who have now decided it's one vote and that's it, that re-voting is somehow undemocratic.
I expect they would also say the right to appeal a court conviction is also wrong; once convicted that's it. Tough shit if convicted on the back of lies and false claims.