You'd be surprised how many Irish (myself included) don't honestly have uniting Ireland on the agenda. The Taoiseach sure as hell doesn't, not with Sinn Fein still out of power.
Scotland will eventually leave, I have no doubt of that.
Wales is, unfortunately, tethered to England near indefinitely. Wood doesn't have the charisma or, frankly, ferocity Nicola Sturgeon does, and the population in general is closer to the English.
That leaves Northern Ireland, who for the most part identify as British much more than Irish, quite like the queen, and don't really want to be joined with us. The Good Friday agreement practically means unless they vote en masse to leave the UK, which they won't over something like Brexit, they're stuck with 'em.
Northern Ireland has one advantage the rest of the UK doesn't - you can quite easily just move across the border to the Republic if you want to stay in the EU. So Northern Ireland has less of a reason to panic and leave the UK when there';s somewhere they can go if it bothers them that much.