There is a good bit of overlap between Ireland, Britain, Scandinavia, and Europe West due to past invasions and migrations. By no means does having only <1% Irish DNA mean that the DNA from those Irish ancestors is missing. Rather, it could just be indicating that you may be descended from groups that invaded and settled in Ireland at later periods, such as Scandinavian Vikings, Anglo-Normans (themselves a blend of Viking, French, and British by that point), English/Scots, or others who came after the original Celtic-speaking population (which also had genetic ties to the Basques of northern Spain as studies have shown).

Also, as was mentioned, DNA inheritance is indeed random. After several generations, certain pieces of DNA get "lost" in the shuffle. That doesn't mean it's not part of your ancestry, just that maybe you lack the genetic markers from that ethnicity.