I expect post actual brexit the problems Ireland are bound to face will result in a desire for change. This however isn't limited to Ireland, or to brexit.
More broadly there is a worrying trend within the western world, a dynamic that is potentially very dangerous.
Governments of all colours and creeds have willingly given up power, whether that power has flowed to supranational bodies such as the EU, multinationals, industry bodies, corporate lawyers, markets or the media doesn't actually matter.
This however has never been adequately explained to voters, hence when things go wrong they expect the government to do something about it, though often they are either totally powerless or too slow to react.
Hence rather than further globalistion, corporatist dogma or devolution the recent trend is toward statists. It's a very strong trend with relative newbies being able to make a link, in a Farage sort of a way, between this powerlessness of the establishment / government / evil multinational and a certain privileged disdain for the ordinary problems of the voters. The newbie claims a virtue from their untainted status, by being uncontaminated, and promises to fix the problems that 'they' don't care enough about.
Corbyn and momentum are excellent examples of this, but so is Trump. It really isn't a left right issue, it's a statist versus globalist one. The swingometer appears to have flipped very rapidly, so much so indeed that it has caught most political wonks with their pants down.
So whether Ireland or the other piigs at some point voter disenfranchisement will likely lead to a virgin candidate, probably as we saw in France with a new party, promising to cure the economic ills with enhanced state control. Its notable that there is barely a strong government in any of the piigs which rather magnifies the effect.
Meanwhile the actual governments, having given away too much power, are almost sitting ducks.
It's a strong trend to the return of the nation state in short, which leaves bodies such as the EU swimming against a very strong tide.