Because a leave vote of 51%/49% could start a civil war.
Politically, giving a region it's own parliament is a much safer bet.
Brexit decided to leave the EU 52%/48%. Several commentators pointed out that if the referendum were held again, it could flip the other direction just on who turned out that day.
Northern Ireland stayed in the UK while the rest of Ireland became an independent nation in the 1921, which started "The Troubles". In 1998 the Good Friday Agreement seemed to have ended the Troubles, after 77 years. The Good Friday Agreement also explicitly allows Northern Ireland to leave and rejoin Ireland with a referendum.
Germany reunified in 1990. It's unlikely there is real political will behind splitting it up again.
Most votes are electing representatives. It's a contentious fight, but they'll have to run again in some years, and voters usually have elections in the mean time to strengthen or weaken the party currently in power.
Stay/Leave votes are one way. The loss is catastrophic. If you're having a Say/Leave vote, there is obviously not a good sense of national unity. All these things mean there's a good chance for violence.