This impasse will be resolved when either politicians in the whole of Ireland learn how to compromise or the Heat Death of the Universe occurs, which ever happens first.
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The situation in N Ireland at the moment is bonkers. NI voted decisively in favour of remaining in the EU, gaining about as much support as the two main (implacably opposed) political parties combined - a rare example of an issue that united both Unionists and Republicans.
And yet, now that the deal is being trashed out in Brussels (or not as the case may very well be), the DUP (who are propping up the current UK government) have decided that they no longer agree with the majority of the people of NI (in wanting to remain in the EU) and are now pursuing the tactic of "We demand to be the same as the UK", even though the UK (though mainly England) voted the opposite way on continued EU membership.
So it is hardly surprising that it smacks of cutting off their nose to spite their face - the DUP will, at a stroke, throw away a possibly unique opportunity to stay in both the UK and the EU because, by virtue of technically remaining in the EU, Northern Ireland would (in their view at least) become more like Ireland than the UK, and they cannot countenance that - they'd rather press ahead with a course of action that their own people don't want than to risk playing into the hands of those who seek a unified Ireland.
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Of course, by effectively offering Northern Ireland a 'special deal' that would effectively keep NI in the EU single market and customs union, the UK government have basically confirmed to other 'Remain' regions (notably Scotland and London) that such a deal is possible... if it can be done for NI, then it can be done for them. The cat is out of the bag on that front, and you can bet that the SNP in Scotland will not forget it or let it go.