A fresh appeal will be held for Ugandan asylum seeker Brenda Namigadde next week.
The 29-year-old lesbian says she will be killed if deported from the UK to her home country.
The appeal will be heard at the Royal Courts of Justice in London on Monday and her supporters are continuing to plead with the UK government to allow her to stay here.
Ms Namigadde was told she could not stay in the UK two weeks ago, when a judge ruled that there was no evidence that she was a lesbian because she did not read gay magazines.
She was granted a temporary reprieve last Friday, while on board a plane that was waiting to depart from Heathrow airport.
If her fresh claim is not allowed to proceed, it is likely she will receive new removal instructions within a fortnight.
This week, Labour MP for Hammersmith Andy Slaughter tabled an early day motion in parliament calling on the government to allow Ms Namigadde, who is one of his constituents, to stay.
It said: “Widespread publicity about Ms Namigadde’s sexuality has placed her at severe risk of harm.”
Mr Slaughter told PinkNews.co.uk: “It is a very high-profile case. Her life is potentially at risk.”
Immigration minister Damien Green has refused to intervene in the case.
Ms Namigadde has also attracted the attention of Ugandan MP David Bahati, who tabled the country’s gay execution bill. He told a journalist that she could return home if she “repents” but will be punished if she does not.
Her supporters are currently trying to track down a Canadian woman named Janet, who Ms Namigadde says she had a relationship with while in Uganda.
According to LGBT Asylum News, campaign group AllOut.org will today launch a new push to ask the government to allow her to stay in the UK.
The organisation sent a 30,000-signature petition to Home Secretary Theresa May last week to ask her to intervene in the case.
A spokesman from gay lobby group Stonewall told PinkNews.co.uk: “We have raised the issue privately with Home Office ministers.”