Suicides are the #2 cause of death in the armed forces, only behind accidents.
In my opinion there are three big problems:
(1) Limited access to healthcare providers. There are hardly any psychiatrists in the armed forces. For example, in 2008 at Lakenheath for example there was 1 psychiatrist for all of England. In Korea there were 2. I can't remember how many tens of thousands of troops they were responsible for, but it was a lot
(2) No confidentiality. The electronic scheduling system (patient appointments and scheduling (PAS) component of CHCS) is incredibly flawed. Anyone with access to the hospital can look up what sort of doctor you have an appointment for. Even though the bases can be fairly large, it's a fairly small community, especially if you're overseas. Imagine having to worry about your coworkers/neighbors spying on you on top of your problems
(3) Vulnerable populations. Only the air force requires a high school degree. You take these young, uneducated people and separate them from their families for years at a time.