My friend's husband is burning out and won't admit it.

Is it possible for somebody suffering from burnout or mental fatigue to live an outward life normally?  My friend's husband does that, but he has emotionally switched off from his wife and 5 children in a big way.  He refuses to admit anything is wrong.  My friend on the other hand blames him and says he chould admit his problems if he chose.   But is it possible he is beyond the point of choice and if so, what can she do to help him?

Yes, it is possible for your friend's husband to be struggling with burnout and not realize it or think that anything is wrong.  Unfortunately, burnout often leads to emotional withdrawal from those one needs most . ..  and this adds the the vicious cycle. 

Demanding that he "admit" he has problems is a waste of time.  Worse, it is not at all helpful and just makes matters worse.  Your friend, with her nagging, has made herself part of the problem.  It is no wonder that he has withdrawn. Demanding that one "admits" one is screwed up is NOT being supportive.  It is being a harpie.  If your friend values her marriage, she needs to do something very different and stop being a nag.

Burnout is a kind of job depression and caused by feelings of powerlessness (helplessness, loss of control).  Being nagged at exacerbates it.  Demanding that one "admit" one is helpless -  that something is "wrong" - exacerbates the situation, especially if that person is a man, and does not increase one's sense of control.  It does just the opposite.

What should your friend do?  Get off of her husband's back would be a big start.  Then SHE would do well to seek counseling for herself - to learn how to be supportive - instead of sabotaging her relationship and treating her husband like a bad boy who needs to "admit" something is wrong.  It is a lot easier to point a finger of blame at one's husband.  One concrete action would be for your friend to force herself to focus on what her husband is doing right and to comment on that ONLY and ignore what she perceives as his wrong doings.   He is not going to re-engage with someone who is continually punishing him - which is what she is doing.