Honestly, I think it might be that the sense of self-preservation is what's holding them back: they do not want to be utterly cut off from their fellow soldier (or sailors, or marines, as the case may be), destroyed in spirit and reputation and, if they have a family, becoming a burden to them as they will incur a dishonorable discharge for so opposing their Supreme Commander.
It's the Big City mentality manifest in the ranks: they are all smashed together but, oh, so alone.
[/theory]
Only if they lose.
Their fate if they don't try is death. It's just slower, and they will have about 1/3 of the US population joining them in whatever version of the killing fields/gulags the likes of Bill Ayres ad his friends have planned.
Win, die on your feet, die on your knees, live on your knees. Not many other options.