Christie Elan-Cane, who does not identify as either male or female, had asked the court in London to rule that Britain's passport application process was "inherently discriminatory".
Individuals only have a choice of male or female on the application, rather than permitting them to mark down "X" for unspecified.
Countries including Canada, Australia, Denmark, Germany, Malta, Nepal and Pakistan all now issue passports with options other than male and female.
Lawyers for Elan-Cane argued the British government stance breached legal guarantees to a private life and the right not to face gender or sex discrimination.
But three senior British judges dismissed the appeal after hearing the case in December.
Elan-Cane, who has fought for legal and social recognition for non-gendered identity for more than 25 years, called the decision "devastating".
"It is bad news for everyone who cannot obtain a passport without the requirement imposed by the UK Government that they should collude in their own social invisibility," the campaigner said in a statement.
The court battle has unfolded over several years after Elan-Cane won the right in 2017 to challenge the policy.
However, the High Court dismissed the bid for a judicial review the following year. The campaigner then appealed against that decision, leading to the latest ruling.
Elan-Cane, who uses the pronouns "per/per/perself" instead of "he/his/himself" and "she/her/herself", said she would continue the legal fight.
"We intend to seek permission for the case to be heard at the Supreme Court," the activist said on Twitter.
'X' PASSPORTS
— Christie Elan-Cane (@ChristieElanCan) March 10, 2020
I regret to inform that the Appeal Court has ruled in the UK government's favour in a judgment handed down this morning.
We intend to seek permission for the case to be heard at the Supreme Court.
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