Traumatic brain injury has been the most common wound for troops deployed to Afghanistan and Iraq, where insurgents turn to concealed roadside bombs to counter the military edge of U.S. and allied forces in face-to-face combat. More than 408,000 American service members have suffered traumatic brain injuries since 2000, some 80% of them concussions, according to the Pentagon’s Defense and Veterans Brain Injury Center.

The Pentagon says most injured recover from concussions within days or weeks, but healing can take more time for those who have experienced multiple concussions.

Veterans groups say effects such as blurred vision or irritability can linger far longer, with complications that ripple into work performance and personal relationships, according to Randy Reese, executive director at the Washington, D.C., headquarters of the million-member Disabled American Veterans.

“It just appears the commander-in-chief is somewhat out of touch regarding the seriousness of this injury,” Mr. Reese said in an interview.