The Romans never truly invaded Ireland, but they did have some forts in Ireland, like one that was [discovered in Drumanagh, near Dublin.] (http://www.archaeologyuk.org/ba/ba14/BA14FEAT.HTML)

However, there's just no real historical evidence that the Romans ever invaded Ireland. [However, there is certainly evidence that they traded and interacted with the habitants of Ireland, but not why they did or didn't invade Ireland.] (http://irisharchaeology.ie/2011/11/roman-contacts-with-ireland/) It's very difficult, if not impossible, to answer this question without speculation. Sorry this isn't the answer you're looking for, but I just wanted to point this out.

Unlike modern strategy gamers, Romans did not invade a place just to paint a map in their colour. Roman wars were fought to pacify hostile tribes so they wouldn't raid settled districts any more; to win agricultural lands for colonists; or to provide personal glory for an emperor or ambitious general. By the time the Romans were even in contact with Ireland, the first two reasons did not apply so strongly any more, and they would have been weak as regards Ireland anyway: Irish soils are too heavy and wet to be much good for the light plows of the time - not to mention the trees! - and the Irish tribes then did not do much raiding across the sea. That leaves glory, but an emperor who wanted to beat up on someone had much easier targets available - Germans, Persians, Dacians. There was just no point in going all the way to Ireland, with a crossing of the dangerous Atlantic, to beat up on some tattooed savages that wouldn't even provide much in the way of impressive loot to be displayed at the Triumph.