Have a friend who served in Afghanistan, he is now a mid-level officer rank and he talked about how bad the suicide rate was among his soldiers. He was going through a rough patch at home and though we didn't talk about suicide with regards to him I can probably guarantee he thought about it. I have seen enough suicides to last me a lifetime. Taking a life and being in violent combat up close is a real hard thing for the human brain.
Beers is always a good ice breaker for guys to open up but generally bad for anyone suicidal. I have to remind myself that if anyone calls me for help instead of saying lets grab a beer I should say lets grab a coffee. With guys especially it can be real hard to bring up the subject, there just seems to be a natural barrier to it, best we can mutter is "you doing ok bro?". I know a guy at work that really seems to despise being at home with his wife and it stresses him out. Other coworkers tell me to stay out of his business when I voice concern but I also feel compelled to do something to read out to him. I don't think him suicidal but I don't think he is in a healthy marriage and if he went through a very ugly divorce and lost his kid who knows where that would push him.
Regarding military and suicide, it's staggering. I know many who have good friends who have taken their lives. Personally, none who are really close friends. I had an uncle when I was little who took his own life, but that was after cancer came back a second time and I believe he had enough.
Everyone will deal with things in their way. As for beers, if that's not right for your or folks around you, so be it. For me, it's a good way to relax and bond with folks, especially my good friends. Sure, if I even suspected someone was suicidal, it would approach things differently. Ever since HS, I've always had folks confide in me. Lately, even my buddies' kids. Sometimes its things I can't really relate to, but I've found that many times it doesn't really matter. Yeah, some are looking for help, but many times I believe many are just looking to vent, validate their thoughts/feelings, know they aren't the only one going through that, etc. In my case, I shared my experience in caring for loved ones and while I was happy to do so, that it took a toll on me. A toll that I didn't really until afterwards.
As for barriers, I can only speak from personal experience. If you're anyone other than close family or friend, one "you ok" is good, second shows you care. Anything beyond that is you not respecting boundaries. You do what you want of course. If someone is ready to open up to you, no amount of "you good bro?" is going to suddenly flip the switch. You've showed that you care, that you are willing to listen, etc. Personally, that's all I think you can do. You start forcing yourself in, personally, that would only make me shut you out even more. I have something on my mind that I'm dealing with, last thing I need is for someone pushing the issue when I'm not ready to open up about it. Anyways, my 0.02. . .