The Technical, Engineering and Electrical Union said it was no longer in a position to fund any further legal action.
This followed the non appearance of any legal representation by the other two parties to the agreement AECI and ECA.
The application to withdraw was opposed on the basis that the TEEU has already exposed other parties to legal costs.
Opposing council said: "The TEEU should have made Justice Kearns aware of their intention to walk away at the hearing in July to fix todays date for the full hearing."
Justice Hedigan decided to allow TEEU to withdraw, and will decide on the issue of costs when judgement is made.
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"This now means that all the three parties, who set up the REA, and fully supported it for the last 19 years are not defending the agreement when its very existence is being challenged," said a TEEU spokesman.
"The TEEU, AECI and ECA fully defended the core concept of this agreement at the historic 13 day Labour Court hearing last January."
National Electrical Contractors Ireland (NECI) has insisted the agreement was registered illegally in 1990.
A Spokesman for NECI said: "We welcome the fact that the injustice it has caused to small and medium electrical contractors, who were never party to the agreement or even aware of its very existence will soon be addressed by the High Court.
"NECI has no doubt that the present legal examination of the setup of the REA in 1990 will expose its many legal flaws."
He continued: "The electrical industry can always be grateful that NECI was formed to correct this imbalance and the ECA and the TEEU have now released that we at NECI will no longer accept that we are obliged to operate our business under terms and conditions into which we have no say."
NECI said it is clear there will be casualties in the employer representation in the near future.
"Those who have stood up to the injustice of this unrepresentative agreement will leap into the future as a strong Employers Association whose number one objective is to ensure a viable environment in which its members can earn a living," added the spokesman.
(PR/BMcc)
