That point was debated a bit around the Quebec independence referendum as well. Is a 51% vote enough of a mandate to leave? If so, would a 51% vote in the other direction a few years later be enough of a mandate to
rejoin? You have a weird unstable situation if support really is close to exactly evenly divided, and stays that way. The pure majoritarian outcome would be that you oscillate between trying to leave and trying to join every few years, vaguely like what happened in Greece 100 years ago when they voted in a referendum to abolish, then reinstate, then abolish, then reinstate the monarchy, the pro- and anti-monarchist forces holding a new referendum every time it looked like public opinion was trending back in their direction. In practice it seems then the really big power comes in choosing when/whether to hold a referendum, e.g. if the Quebec referendum had come out 51-49% in favor of leave, independent Quebec would probably avoid as much as possible allowing a "rejoin Canada" referendum to ever be held, lest it come out 51-49% in the other direction.
Probably some mathematical voting theory person has formalized this kind of question in terms of something like sampling and stable outcomes, but I'm not quite sure what keywords to look for there.