He claimed he would suffer irreparable harm if he were sent back to the US and said he sought refuge in Canada because the US army wanted him to participate in what he called an "illegal war of aggression in Iraq".
The ASFC arrested Long last October after his request for asylum was rejected and he was ordered to leave Canada.
On Monday, a federal court in Vancouver refused to suspend the extradition order.
Judge Anne Mactavish said he had not convincingly proven that he would suffer irreparable harm if he were extradited.
The judge acknowledged that the number of deserters tried by the US military justice system had risen in the United States since 2002, but most were not punished for deserting and even fewer were jailed.
From 2002 to 2006, about 94 per cent of US deserters were given "a less than honourable discharge from the military", Mactavish said in Canadian media.
Long was among some 200 American deserters believed to be in Canada in an effort to avoid service in Iraq. So far, Canadian immigration officials and the courts have rejected efforts to grant them refugee status.
During the Vietnam War, up to 90,000 Americans, most of them trying to avoid the military draft, successfully sought refuge in Canada.
The majority of them returned home after the US declared an amnesty in the late 1970s.
Return to base
Sarah Bjorknas, a co-ordinator for the War Resisters Support Campaign, said Long would be returned to his unit based in Fort Knox, Kentucky.
She said Long's punishment for deserting would be up to the company commander and could include court martial and prison time. He could also still be deployed to Iraq.
Bjorknas said Long had apparently been moved between several jails in British Columbia, adding that the moves frustrated the group's attempts to provide Long with assistance.
Last week, Canada's Federal Court granted Sergeant Corey Glass, 25, a US national guardsman, a stay to his deportation order while the court decides whether to hear his case.
Glass had refused redeployment to Iraq.