There have been calls on the Government to ensure the country is better prepared to mitigate the disruption caused by severe weather events.
Opposition parties said State supports need to be made more readily available and that increased finance should be provided to local authorities for preventative measures.
ESB Networks said this evening that 45,000 customers were still without power.
Many others have had supply returned in recent days, only for further service disruption to follow.
The company said that following restoration works on main lines, further interruptions are sometimes necessary, to ensure crews can carry out repairs elsewhere safely.
Amid the incremental progress being made, attention is shifting to the ways in which the country can better prepare for future storms.
Sinn Féin sought the distribution of goodwill payments to households who have been without power, saying this should be funded by energy companies.
Read more: 'We're cross with the system' - A week in the aftermath of Storm Éowyn
The party's TD for Galway-Roscommon Claire Kerrane has written to the Taoiseach, on behalf of Sinn Féin representatives in the Connacht and Ulster area, calling for a series of measures to guard against a repeat of the upheaval being experienced in recent days.
There have also been calls for enhanced provision of services in rural areas.
Aontú TD for Mayo Paul Lawless said there was a huge level of frustration, especially in relation to vulnerable and medically compromised people, who he said, were not getting the attention they deserved.
Mr Lawless said a lack of generator capacity and a delay in accessing such infrastructure was a major source of difficulty.
He said that recent initiatives had "incentivised people to be totally reliant on the grid and we've seen that extremely exposed".
"The truth is we live in a rural, dispersed country and we need to ensure people have back up generators to have support when their power is knocked out," Mr Lawless added.
With thousands now into their second week without vital services, the Department of Social Protection said those who have had to source hotel or B&B accommodation, as a result of the disruption, will be given financial support, once they can provide confirmation of their bookings.
It is understood claims will be cross referenced with MPRN details of individual electricity customers.
