The regulator ruled in May that the group, which supports women in the Catholic church and campaigns for the ordination of women as priests, could not be granted charitable status.
In June, CWO appealed against this to the charity tribunal, arguing that its work provided a public benefit by advancing the Christian faith. It said the regulator had overestimated the scale of its campaigning work and underestimated its other work in supporting female lay members of the Catholic church.
But the group has dropped its appeal because of worries about the time and effort that would be required to argue its case before the tribunal.
Gareth Morgan, senior partner at the charity consultancy the Kubernesis Partnership, who was representing CWO on a pro-bono basis, told Third Sector: "We submitted our appeal and the Charity Commission responded by submitting huge reams of material that we would have had to respond to, some of which was based on highly complex pieces of case law.
"CWO has just one part-time member of staff and is mostly run by volunteers. When we made the appeal, it took up everyone’s time and was affecting the rest of our work. We realised this would have continued to be the case for some time if we had continued with the appeal.
"We had strong arguments, but the trustees decided it was not worth the effort and the uncertainty."
Morgan said charitable status could have allowed the group, which has an annual income of less than £10,000, to raise about £1,000 more a year through Gift Aid. It would also have allowed the organisation to prioritise seeking legacy donations, he said.
He said he was disappointed that the appeal had to be dropped, because the charity tribunal had been set up to offer low-cost, straightforward access to redress for small charities.