The ESB say "small pockets of customers" could be without power for a second night.
It says its crews are working to restore power to 1,500 affected customers after Storm Doris.
More than 54,000 have now had their power restored since Thursday.
The supplier says its crews have been working since early morning on more than 600 individual fault sites.
"Crews are working tirelessly to get customers restored as soon as possible", it says.
But it says that due to the severity of the damage, some may be without power for a second night.
Affected customers are located in:
- Julianstown
- Drogheda
- Navan
- Balbriggan
- Swords
- Ashbourne
- Mulhuddart
- Arigna
- Carrick on Shannon
- Mohill
- Ballaghadereen
- Parts of Castlebar, Tuam, Cavan, Longford and Sligo
Crews have been deployed to these specific areas to assist with the high number of faults.
Customers without power can check for updates on when their supply is expected to be restored at the PowerCheck website.
For faults that are not appearing on Powercheck, customers are asked to log a fault at ESB Networks or call 1850 372 999 or +353-21-2382410.
