Earlier this year I was also trying to research a family member who died there in the 1920s, but couldn't get anywhere. I was in contact with a Priest, the former chaplain there, who had a lot of dealings with handling the archives, and the records seem to have been transferred to the National Archives. I've sent several emails to the National Archives just trying to confirm if they had the records, but didn't even get a reply.
I've since seen in the National Archives 2013 Director's Report:
"Grangegorman Hospital Archives: Wellcome Trust project, years 1 and 2
Two grants awarded by the Wellcome Trust in 2012 fund work on the archives of
Grangegorman Hospital. The work is carried out by a project team consisting of an
Archivist, a Conservator, a Project Assistant and a Preservation Assistant. Good progress
was made in the cleaning, arrangement, listing and conservation of the collection by the
end of 2013.
Grangegorman Hospital was founded as the Richmond Asylum in 1814 and became the
largest and most important psychiatric hospital in Ireland. The archives are the most
voluminous collection of hospital archives known in Ireland. We are grateful to the
Wellcome Trust and to the management team in Grangegorman Hospital (St Brendan’s)
for their support."
So, as far as I can ascertain, in the last few years the papers have changed hands and are not accessible at the present time. Hopefully the conservation/cataloging process will be done soon though. (Knowing the National Archives, however, I somehow doubt it).
My only worry is that now that it is in the National Archives far stricter rules will apply in accessing material in terms of protection of privacy, etc. for patients from the 1910s on.