Generally speaking, those that are likely to take advantage of various programs by themselves have already done so. They aren't a big secret or anything. A visit to the local Social Security office is about all it takes to get connected. Maybe the VA if your military. It can take a day or so, and be a real PITA, but nothing that's super hard to manage. So the people who don't get in these programs are mostly, for whatever reason,the types that don't want to go.
It's hard to say, because it's an emotional thing, not a rational thing, but I think of it as two broad categories of resistance... I tend think of them as "structure" and "content"[1].
Some people have physical, structural problems with their brains -- they had a serious brain injury, a concussion, or stroke, or something; and they are functional enough to stay out of prison or not cause obvious problems, but their brain is shot or they just can't get themselves to focus for long enough to make any real headway with getting help on their own. I'd bet some just have ADHD, or some other organic/structural problem with their brain.
Many of seem to have had a bad childhood, or a real bad experience at some point, and it left them feeling so poorly about themselves that they just expect the world to crap on them, like there is nothing they can do about it. They might descend into depression, or addiction, or spin off into some fantasy world, or deal with it in some other destructive way. I've noticed that the earlier things went wrong then the worse the effects seem to be, but this is strongly dependent on the person and what actually happened, and their current environment that it's hard to say anything useful.
So that's how I think about it, but what I do is to try to gently push people in the direction of getting help and making their life better, sometimes hold their hands, and not worry too much about who it is or their current situation in life. Sometimes I'm better than others, and I'm better with some people than others, so I don't beat myself up if I can't really help.
[1] Just to get a little philosophical - they aren't really separate, just a useful way of thinking about what's going on. I'm a Buddhist, and the structure/content idea helps me to see how my own mind works. For example, if I drink a lot of coffee and get really cranked up -- that's more of a physical/structural explanation of why I experience the world a certain way. If I have certain thoughts ("I'll never get this damn code right", or "my life is crap") then that leads me to experience the world a certain way -- neither mean the world actually is that way.
