It happens pretty soon (ch 6) -- I just grabbed the ebook and am skimming the scene for you. Basically he gets called into Illyan's office and he thinks he's there to get his next Dendarii mission but it turns out Illyan knows and is basically all "so you lied to me and you're not medically fit and you have to resign and take this medical discharge and hand in your eyes." Miles tries to protest, ends up having a seizure in Illyan's office, and resigns and leaves. He has to walk out in view of a couple of ImpSec officers, though. Including Galeni.
He actually doesn't spend that long moping about because Ivan and Galeni come to Vorkosigan House and dump him in an ice bath and then try to cheer him up, which is nice of them. And then he's like, okay, maybe I can try being Miles Vorkosigan instead of Naismith for a change.
Most of the actual plot revolves around things that happen to Illyan. Sad things! But he is okay in the end too, and maybe happier. Like Miles is!
[ETA: Also Galeni is pretty heavily in the plot, in case you are also prone to worrying about him.]
Oh, and if you haven't read "The Mountains of Mourning" (the story where Miles investigates an infanticide) you will probably want to have read that before Chapter 10 or so because he goes back to see the people from that story.
(If you're squicked by people doing things that might get them into social trouble as well, the Vorkosigan novel you might have difficulty with is A Civil Campaign, which hits my embarrassment squick so hard I have to skip several scenes every time. That one is a comedy of manners where key scenes hinge upon Miles (unsuccessfully) trying to keep his romantic intentions secret and the reveal is supposed to be funny and I can't read it and Mark also has a subplot that is supposed to be funny and I can't read that either.)
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He actually doesn't spend that long moping about because Ivan and Galeni come to Vorkosigan House and dump him in an ice bath and then try to cheer him up, which is nice of them. And then he's like, okay, maybe I can try being Miles Vorkosigan instead of Naismith for a change.
Most of the actual plot revolves around things that happen to Illyan. Sad things! But he is okay in the end too, and maybe happier. Like Miles is!
[ETA: Also Galeni is pretty heavily in the plot, in case you are also prone to worrying about him.]
Oh, and if you haven't read "The Mountains of Mourning" (the story where Miles investigates an infanticide) you will probably want to have read that before Chapter 10 or so because he goes back to see the people from that story.
(If you're squicked by people doing things that might get them into social trouble as well, the Vorkosigan novel you might have difficulty with is A Civil Campaign, which hits my embarrassment squick so hard I have to skip several scenes every time. That one is a comedy of manners where key scenes hinge upon Miles (unsuccessfully) trying to keep his romantic intentions secret and the reveal is supposed to be funny and I can't read it and Mark also has a subplot that is supposed to be funny and I can't read that either.)