It took a half an hour for the ambulance to be dispatched and take the man from one building to the other, which is about a five-minute walk, officials at the hospital said.
Kirtland Air Force Medical Group personnel performed CPR until the ambulance arrived, VA spokeswoman Sonja Brown said.
Staff followed policy in calling 911 when the man collapsed on Monday, she said. "Our policy is under expedited review," Brown said.
That policy is a local one, she said.
The man's name hasn't been released.
News of the man's death spread Thursday at the Raymond G. Murphy VA Medical Center among veterans who were visiting for various medical reasons.
Lorenzo Calbert, 65, a U.S. Army veteran of the Vietnam War, said it was sad that a fellow veteran had to die so close to where he could have received help.
"There's no reason for it," he said. "They have so many workers. They could have put him on the gurney and run faster than that ambulance."
The death comes as the Department of Veterans Affairs remains under scrutiny for widespread reports of long delays for treatment and medical appointments and of veterans dying while on waiting lists.