Officials at the hospital said 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.
VA spokeswoman Sonja Brown said Kirtland Air Force Medical Group personnel performed CPR until the ambulance arrived.
She says staff followed policy in calling 911 when the man collapsed on Monday. "Our policy is under expedited review," Brown said.
The man's name hasn't been released.
The death comes at 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.
A review last week cited "significant and chronic system failures" in the nation's health system for veterans. The review also portrayed the struggling agency as one battling a corrosive culture of distrust, lacking in resources and ill-prepared to deal with an influx of new and older veterans with a range of medical and mental health care needs.
The scathing report by deputy White House chief of staff Rob Nabors said the Veterans Health Administration, the VA sub agency that provides health care to about 8.8 million veterans a year, has systematically ignored warnings about its deficiencies and must be fundamentally restructured.