At the peak over 117,000 homes were without power as Storm Emma lashed the country
The ESB says 30,000 additional customers have lost electricity since Friday morning.
In its latest update, the utility says 34,000 homes, farms and businesses are without power.
It says ongoing snowfall is causing new faults - mainly in Enniscorthy, Arklow, Portlaoise and Cork.
In a statement, ESB says: "Due to these new faults, access issues, and worsening weather in the South East, it will be tomorrow at the earliest before some customers will get electricity back.
"Cork, Enniscorthy, Arklow, greater Dublin area and eastern counties of Leinster the main areas affected".
It says since Friday morning, "good progress" have been made on the faults in the greater Dublin area.
However, worsening weather in the south east has caused power to be lost to an additional 30,000 customers.
"We will continue to work with the emergency services and local authorities to ensure the safety of the pubic and to minimise disruption and are working with other state agencies to help us gain access."
Ice and snow on the roads is slowing down repairs, the utility says.
ESB Networks staff are working through extremely challenging conditions to safely restore power to the 26,000 remaining customers without power due to #StormEmma. Please check https://t.co/hWag1LtpfF for outage info and updates, and log faults on https://t.co/57xk3OozCW #StaySafe pic.twitter.com/sQSaAYW6eU— ESB Networks (@ESBNetworks) March 2, 2018
Updates and estimated restoration times can be found on the Powercheck app and www.esbpowercheck.ie
Derek Hynes from the ESB explains how faults have occurred:
“It was wind plus snow really,” he said.
“Normally when we get wind, we get trees that come down on the network and they are what causes the majority of our faults.
“We are seeing some branches from trees which are being being weighed down by the snow coming down on our network.”
Additional reporting: Jack Quann