ESB Networks has said customers in some rural areas in the south of the country may be without power until Thursday.
Storm Darwin caused widespread damage to the electricity network, with the south worst affected.
More than 25,000 customers remain without power this morning.
The main faults are in Tralee, Newcastlewest, Fermoy, Dunmanway, Killarney, Bandon and Waterford.
Bevin Cody of ESB Networks said: "At this stage, progress is going to be very slow because the number of customers per fault is falling.
"That means the crews could spend half a day trying to remove a tree and restore power to only a couple of customers.
"We will be getting to most isolated areas by Tuesday or Wednesday of this week. Hopefully everybody will have their power back by Thursday."
For updates on estimated restoration times, see here.