A major problem for the military is the availability of guns (and people who are effective at firing them). In the UK we used to kill ourselves with gas from the stove (it had carbon monoxide in it) - when gas stopped having carbon monoxide people thought - 'well people will find another way of killing themselves' but they didn't - availability of way of killing yourself was a factor in suicide. There's no obvious solution for the military, since they need guns. However, we can say that as a group they are more likely to kill themselves as they have an effective means to commit suicide when they are depressed. In the way an office worker does not.

Wikipedia article on this subject:

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Lethal means reduction [edit] Means reduction, reducing the odds that a suicide attempter will use highly lethal means, is an important component of suicide prevention.[17]

For years, researchers and health policy planners have theorized and demonstrated that restricting lethal means can help reduce suicide rates, as delaying action until depression passes.[18] There is strong evidence that restricted access at so-called suicide hotspots, such as bridges and cliffs, reduces suicides, whereas other interventions such as placing signs or increasing surveillance at these sites appears less effective.[19] One of the most famous historical examples, of means reduction, is that of coal gas in the United Kingdom. Until the 1950s, the most common means of suicide in the UK was poisoning by gas inhalation. In 1958, natural gas (virtually free of carbon monoxide) was introduced, and over the next decade, comprised over 50% of gas used. As carbon monoxide in gas decreased, suicides also decreased. The decrease was driven entirely by dramatic decreases in the number of suicides by carbon monoxide poisoning.[20][21]

A photo illustration produced by the Defense Media Agency on suicide prevention In the United States, numerous studies have concluded that firearm access is associated with increased suicide completion.[22] "About 85% of attempts with a firearm are fatal: that’s a much higher case fatality rate than for nearly every other method. Many of the most widely used suicide attempt methods have case fatality rates below 5%.".[23][24]

http://en.wikipedia.org/wiki/Suicide_prevention