I do not think that the increase of suicides in the military has much to do with the Internet.
It may be a result of the fact that people have smaller families and therefore fewer relatives to provide aid and comfort to them. It also might have something to do with the fact that the population as a whole is less religions, and the taboo against suicide are less strong.
There are a lot of soldiers who were horribly wounded and yet recovered because of better and faster medical care. In previous wars a lot of these people would have died, but now they are alive, but horribly maimed.
Those are some of my speculations. Obviously, there is a reason for the increased frequency of suicides.