The political arm of the 2 million-member Veterans of Foreign Wars endorsed President Reagan for reelection last week. The endorsement was not exactly a surprise, because the VFW has been one of the president's strongest supporters since it ended its nonpartisan tradition to support him in 1980.

What has surprised several top Veterans Administration officials is that Democratic presidential nominee Walter F. Mondale has not capitalized on what some agency officials see as a potential weakness for Reagan among the nation's 28.2 million veterans.

These officials contend that if Reagan is reelected he would be much more inclined than Mondale to reduce VA benefits. An estimated 40 million persons are aided by VA medical, benefit and loan programs.

This summer, the Reagan administration delayed releasing a study that predicted that the agency's $25.8 billion budget might have to grow by 61 percent by the year 2000 because of the coming surge of elderly World War II and Korean War veterans. By 1990, one of two American men age 65 or older will be eligible for free VA medical care, when beds in VA facilities are available.

Neither political party has addressed the "graying veteran problem." The Republican Party platform, in effect, skirts the issue, as did Reagan when he recently addressed the annual conventions of the VFW and the American Legion.

The Democratic platform says veterans should receive the "highest quality health care available" without explaining how the government will pay for it.

Some career VA officials predict that, if Reagan is reelected, the Office of Management and Budget will urge him to adopt a number of cost-cutting recommendations that the Congressional Budget Office made last April.

Among other things, the CBO recommended that veterans be required to reimburse the VA for medical care if they are covered by Medicare or have private health insurance. It also proposed providing free VA hospital care only to veterans who are poor or suffering from injuries directly related to their military service.

One longtime VA official privately suggested that both candidates are sidestepping the issue because "neither wants to admit that VA benefits are probably going to have to be cut sometime soon." VIETNAM VETERAN STUDY . . .

The VA has awarded a $3.6 million contract to Research Triangle Institute in North Carolina to study post-traumatic stress disorder and other readjustment problems among Vietnam veterans.

The study calls for interviews with 2,900 Vietnam-era veterans, including women, minorities and incarcerated veterans.

Studies by the VA's Readjustment Counseling Service suggest that 20 percent of the 4 million veterans who served in Indochina between 1964 and 1975 have "substantial war-related psychological difficulties that are impairing their lives."

The problems include nightmares, flashbacks, insomnia, anxiety, depression, irritability, alienation and an inability to resume a productive life.

Some psychiatrists and veterans recently have challenged the VA's figures, saying they are too high.

The study, mandated by Congress last year and scheduled to be completed in late 1987, is supposed to identify what percentage of veterans may suffer post-traumatic stress disorder. WOMEN USE VA BENEFITS LESS . . .

An internal VA report has found that female veterans do not use VA medical facilities to the same extent as male veterans. The VA's first study of women veterans found that women make up 4.1 percent of the veteran population but only 2.1 percent of the patients in VA hospitals.

VA Administrator Harry N. Walters said VA medical centers have been ordered to identify how to make their facilities more attractive to women veterans. Walters said VA hospitals have been instructed to take steps to ensure women's privacy when they visit the facilities. Many hospitals also are beginning to offer gynecological care.