I also provide input to the appropriate agency/unit when they send someone over that I identify as having some potential problems down the road - that may cost their compadres or themselves. Suicide is taken VERY seriously...but like so many other problems people exhibit, I think those around the person in question may err towards underestimating the internal battle going on. One must never be embarrassed to ask and act.
At my final training command we had three instructors (one of whom had just transferred to sea duty) commit suicide over a three-year period. Two were submariners and a third was a Navy diver. All were fairly experienced-- a chief petty officer and two E-6s with each over a decade of service. All had been Sailors of the Year at various commands and were considered leaders (especially the CPO, who was legendary around the waterfront). No warning signs, no "cries for help", not even a clue (I had to conduct one of the investigations and assist investigators with the other two). All planned ahead. All used high-powered handguns against their temples. All made sure that there wouldn't be any physical mess to clean up. One of them killed his wife and shot her boyfriend into quadriplegia before killing himself.
In each case there was no indication that anything was wrong or even weighing on their minds. All three had completed physical exams, chain of command interviews, and psychiatric interviews before becoming instructors (in the case of the killer, less than a week before). There wasn't even a whisper of hope for anyone to have an opportunity to intervene.
During the subsequent investigations it became clear that for two of these shipmates there were "little" problems, that they nudged aside (or under the rug) during sea duty, that could no longer be ignored on shore duty. One problem source was an abusive CO and two were marital. All were well-known at the time and all three appeared to be successfully dealing with their issues. (The E-6s had even attended the CPO's funeral, seen the effect of his actions on his family, and knew why he had killed himself.) Yet despite their appearances of coping, a short time later each shipmate had been subject to a triggering event that caused them to commit to a course of action exactly as if their decisions had been taken from a Navy standard emergency-procedures handbook. They had thought things through and two of them even evaded security forces to carry out their actions. When the triggering events happened they didn't call anyone to discuss it. Just like their training they acted quickly, firmly, and with no hesitation.
I'm no longer a believer in suicide "prevention" training. I won't even listen if the trainer has never known someone who committed suicide. If a person wants help then they'll either give pretty straightforward clues or they'll just come right out and ask for it. If someone's already made their contingency plans, however, then we won't be able to do a thing unless Murphy's Law intervenes.
I have learned to trust my instincts, no matter how anal they may appear to be. If something doesn't seem right then by golly, it sure isn't.