"We consider it an abject tragedy that so many of our veterans return home, after risking life and limb to defend our freedom, only to be stripped of their Second Amendment rights because they need help managing their compensation," Chris Cox, the NRA's chief lobbyist, wrote last year in an editorial.
The NRA did not respond to queries from the AP about Coburn's latest effort.
Dan Gross, president of the Brady Center to Prevent Gun Violence, said gun control advocates consider the VA's current policy reasonable.
"We're talking about people who have some form of disability to the extent that they're unable to manage their own affairs," Gross said. "If you're deemed unable to handle your own affairs, that's likely to constitute a high percentage of people who are dangerously mentally ill."
Tom Tarantino, chief policy officer for Iraq and Afghanistan Veterans of America, said veterans with a traumatic brain injury or post-traumatic stress disorder but who pose no threat to others are possibly being barred from gun ownership. The current restrictions might even be a disincentive for veterans to seek needed treatment, he said.
"We want to remove these stigmas for mental health treatment. It's a combat injury," Tarantino said. "They wouldn't be doing this if you were missing your right hand, so they shouldn't be doing it if you're seeking treatment for post-traumatic-stress-disorder or traumatic brain injury."
VA officials have told lawmakers they believe veterans deemed incompetent already have adequate protections.
For example, they said, veterans can appeal the finding of incompetency based on new evidence. And even if the VA maintains a veteran is incompetent, he can petition the agency to have his firearm rights restored on the basis of not posing a threat to public safety.