The criteria need to be added to the registry has gotten more stringent over time. I think 2005 was when the current guidelines went into effect.
I am a natural born citizen of the Republic of Ireland (born in Dublin to Irish parents). I am also a naturalized citizen of the USA (was able to keep my Irish citizenship due to an agreement between the countries).
I was able to have my children added to the registry of foreign births and claim their Irish citizenship through my status as a natural born citizen (even though they were born in the US). They will we able to add their children to the registry for citizenship through me as well.
My siblings, who were born in the US, were able to apply for and obtain Irish citizenship through our father's status as a natural born citizen. Their children, my nieces and nephews, can apply for citizenship through my father (their grandfather). However my siblings' grandchildren will not qualify for Irish citizenship (unless the kids marry a citizen) while mine will, as the criteria currently stands.