Should countries let military prisoners kill themselves?

Solitary confinement probably doesn't prevent death by suicide.

Solitary confinement and 24 hour arm's length supervision might, while it's happening. But it doesn't do anything to prevent the desire and probably makes the thought worse.

There are probably stats on it. I'd have thought solitary would reduce immediate success in suicide and hence also reduce immediate desire. But yes, it's going to be very bleak to be under that sort of regimen and I'd also expect the thought to be worse.

Has nothing to do with my comment.

It reflects on an obvious potential outcome of some alternate methods of punishing the suicide attempt.

How would you handle the situation?

Yes.