For a pub established in 1938 that operated at least 50 years much doesn't exist in the way of google records. However, Sunpost June 8, 2006 archives report in a blurb entitled Feeding Frenzy that "The Quarterdeck Seafood Bar and Neighborhood Grill, founded in 1966, recently opened its first Miami-Dade County location on South Beach. Founder Paul B. Flanigan decided to open a Quarterdeck restaurant in Miami after partnering with Ben Wagman. The Quarterdeck found its new location at the Wagman family's Historic Irish House Pub that operated for 67 years on Alton Road."
According to the math on that, the Irish House Pub closed in 2005.
There's also this reference we found from a July 22, 1999 Bomp List message board thread entitled "Re: bowling with the little balls" authored by Ivan Osorio. It reads...
"The Irish House Pub in Miami Beach (a cool place several blocks away
from the glitz of SoBe), used to have a bumper pool table as late as a
year ago, but it was gone the last time I went. That's a game I'd like
to see come back."
Finally here are ads that appeared in the same column as the one for the Irish House Pub on that same fateful week in 1988.