The human rights group did not have the legal standing to make the appeal, the Supreme Court said in its ruling.
Despite the obvious point that the Northern Ireland Assembly has not been in existence for over a year and doesn't look likely return in the near future, and the fact that it failed to act for many years before then, the fundamental point is that access to abortion is a human rights issue.
Since last month's referendum in the Republic, Northern Ireland is the only part of the United Kingdom and Ireland where termination is restricted to cases where there is a threat to a woman's life or serious risk to her physical or mental health.
The majority of judges ruled that the country's abortion law breaches Article 8 of the European Convention on Human Rights (ECHR), by not allowing abortions in cases of sexual crime (rape and incest) and fatal foetal abnormalities.
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The Deputy President of the Supreme Court, Lord Jonathan Hugh Mance, said that "the present law clearly needs radical reconsideration".
"This must be the final nail in the coffin for Northern Ireland's abortion ban".
British-ruled Northern Ireland is left as the only part of Britain or Ireland with such a restrictive regime, after voters in the Irish republic backed the removal of a ban in a landslide vote last month that sparked calls for change in the North.
Despite this, numerous judges said the existing law was incompatible with human rights law in situations of fatal foetal abnormality and sexual crime.
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As a result, the judges did not make a formal declaration of incompatibility, which would normally lead to a change in the law.
The referendum inspired a similar debate in Northern Ireland with some calling for reform while others like the Democratic Union Party remain opposed to changing the existing law. Two judges went even further and held that the law in Northern Ireland is also incompatible with the prohibition on torture.
The UK Government has resisted calls to step in and legislate amid the ongoing powersharing impasse in Northern Ireland, insisting that any decision on abortion in the region has to be taken by locally elected politicians at Stormont. Theresa May can no longer sit back and do nothing whilst countless women continue to suffer on her watch.
"A majority of the court dismisses the appeal", notes the Supreme Court statement.
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Abortion laws were relaxed in the rest of the U.K in 1967, but that legislation was never applied in Northern Ireland, which had its own parliament between the partition of Ireland in 1921 and the imposition of direct rule from London 50 years later.