To say that war does not have any influence on suicides would, in my opinion, be an ignorant statement and assumption.
When we see no other way out of a bad situation, we have exceeded our capacity to cope and manage our personal pain. I understand the consideration for taking ones life comes from an overwhelming sense of hopelessness. I comprehend this from a personal perspective and a deep realization to "know" the thought of "if I just pull the trigger, the relief I would feel" to ease my emotional agony.
Generally, no one factor precipitates the killing of ones self, to say otherwise would probably be foolish. To discount a soldiers or veterans taking of their own life because the last thing to happen to them was the death of their dog, would be to dishonor their service and sacrifice. Just as no one event can be attributed to a suicide, neither can one crisis be excluded.