Merv and Nikki Kenward, supported by the Christian Legal Centre, originally began legal proceedings after the Director of Public Prosecutions Alison Saunders amended the prosecution policy for assisted suicide in October 2014. Their original request for a judicial review on the change was rejected.
Mrs Kenward opposes assisted dying and argued Alison Saunders' change has meant medical professionals who helped patients to die are now less likely to be prosecuted.
The former theatre manager, who suffers from Guillain-Barre Syndrome and is wheelchair-bound, said the 2014 change has left vulnerable people "at risk from dodgy doctors".
Her claim corresponds with recent figures revealed by The Economist which found that, while an increasing number of reports of assisted suicide are being brought to police, less prosecutions are taking being made.
It prompted the magazine to claim police forces and the Crown Prosecution Service are "turning a blind eye" to assisted suicide.
On Tuesday, the Court of Appeal dismissed an attempt by the Kenwards to win permission to contest their original judicial review ruling.
Lord Justice Longmore, sitting with Lord Justice Kitchin, said it would be "futile" to grant permission as the inevitable result would be that the High Court decision would be upheld.
She said: "Although it does raise difficult and delicate issues, it does seem entirely inappropriate that the case should go any further."
The Kenwards, from Aston on Clun, Shropshire, said they were "disappointed" with the outcome.
