Computer hacker Gary McKinnon "has no choice" but to refuse a medical test to see if he is fit to be extradited to the US, his mother has said.
Janis Sharp said it was "an impossibility" because the expert chosen by the Home Office had no experience with Asperger's syndrome.
Mr McKinnon, from north London, admits hacking US military computers but says he was looking for evidence of UFOs.
If he is convicted in the US, he could face up to 60 years in jail.
The Home Office said the matter would be discussed at a hearing at the High Court on 24 July.
At the last court hearing on July 5, judges were told Theresa May was "close" to making a decision.
But Mrs May said she was "personally concerned" he had not been examined by a Home Office-appointed medical assessor, to decide whether there was a risk of suicide if extradited.
His family say the Home Office expert, Professor Thomas Fahy, has no experience in uncovering suicidal tendencies in Asperger's syndrome patients.
Ms Sharp told BBC Three Counties Radio: "It is not a refusal, he had no choice - it is an impossibility because the assessment they want him to have is by someone who has no experience and wouldn't be able to diagnose his suicide risk."
Mr McKinnon, 46, had three medical examinations in April by three leading experts in Aspergers and suicidal risk, Professor Simon Baron Cohen, Professor Jeremy Turk and Dr Jan Vermeulen.
They concluded Mr McKinnon was at extreme risk of suicide if extradited and he was currently unfit for trial.
The family's decision is supported by the National Autistic Society, which has written to the Home Office recommending alternative experts.
At the High Court hearing earlier this month Hugo Keith QC, appearing for the home secretary, said the case had important implications for Britain's extradition laws.
The judges heard the joint current view of two psychiatric experts - Professor Thomas Fahy and Professor Declan Murphy - was that Mr McKinnon's suicide risk was "moderate".
But Dr Jan Vermeulen, one of the medical experts appointed by Mr McKinnon's advisers, asserted for the first time that he was unfit to plead and stand trial.
Mr Keith said there was lack of supporting evidence for that view, but a fresh examination could lead to a resolution of the differing views.
Mr McKinnon's family had until 19 July to agree to the new examination.
Mr McKinnon, who hacked into the US computers in 2002, has been fighting extradition since 2006.
Ms Sharp added: "Gary has endured 10 years of mental trauma and has lost 10 years of his youth. We so need a good end to this.
"I'm sure that Theresa May will do what's right, and make a just and compassionate decision now and allow Gary to begin to regain some of the life he has lost."
A Home Office spokesman said the home secretary would make a decision as soon as possible.
"This is a complex case, in a complex area of the law, and a large amount of material has been submitted, some of it relatively recently.
"She needs to consider all the material carefully before making a decision."