The Office of Public Works says it is hoping to re-open Sceilg Mhichíl to visitors on schedule this weekend, despite another rockfall there yesterday.
There has been renewed interest in the UNESCO World Heritage Site after it featured in the last Star Wars movie.
A rockfall on the island in mid-March forced the OPW to announce then that it would have to postpone the re-opening of the island to visitors in May.
As well as a UNESCO World Heritage site, Sceilg Mhichíl is also a national monument and attracts around 12,500 visitors a year.
Its birdlife and monastic site, which dates from the 6th Century, are world famous.
Yesterday the OPW announced in a statement that repairs to a safety wall and to the pathway to the monastic settlements had been completed.
However, there was a further rockfall affecting the pathway yesterday evening.
Workmen have been trying to repair the damage since then.
The OPW says it is hopeful that the damage will be repaired in time for the scheduled opening of the island to visitors on Saturday.
