For so much, I zoom in straight to
motive:
"What is the person looking to get out of this situation, what is their reasoning--whether they can verbalize it or not?"
If you want him to share as evidence of your intimacy (I need to know you trust me, why won't you open up to me?) then you're taking the wrong tack. Women might see the sharing of thoughts and feelings as a metric on how strong or good your thing is.
Men usually demonstrate this through actions--taking care of her needs physically / financially, being reliable, being around, trying to help her fix problems, etc. and get very frustrated with a bunch of talk that doesn't add up to a conclusion / change / resolution.
If you really want to help the situation, all you can do is not be a source of stress or concern in his life, and be a source of comfort. Feed him good food, rub his back, fuck his brains out (this is a huge source of stress relief for most men LOL), treat him to something he really likes--movie, tickets to a game, etc. Do NOT nag. Do NOT pick fights. Do NOT make his problem some kind of referendum on your relationship. DO make his life as pleasant as possible so he can focus on fixing his problems. Who knows, he might even open up to you in the process.
If you are concerned about his mental health, and you are in his life deeply enough to know who his friends and mentors are, express your concerns to them--hopefully without coming off controlling or intrusive--and encourage them to check on him. There are guys who open up to women more than men, and guys who open up to men more than women. If you have the second kind of guy, encourage his support system to step up and check on him.
That's all I got on it.
[EDIT:] What a lot of women don't understand about men (and themselves) is we are rarely comfortable showing weakness to you, because 80-90% of women WILL lose respect for you, even the ones who swear up and down they want to see your vulnerable side. This is a big reason men don't often like discussing their problems with their women unless they are absolutely sure their lady isn't gonna hold it against you down the line.

"
Remember when you fucked up our savings that time, and we had to ask my uncle to help you restructure our checking and savings? THAT'S why I don't lend you money..." etc (purely hypothetical LOL)