Greetings!

Sir/mam, there is nothing that will happen even if you don't appear for the examination without siting any reason whatsoever.

Your old result will stay as it was if you don't appear.

Now if you really want to appear for improvement exam and are not able to do so because of valid health reasons, then you can try mailing CBSE on the mail ID that is there on their Website, you can describe your problem and your desire to appear for examination, and wait for their response.

Although as I said even if you don't to all this, nothing will happen your old result will stay as it was, and is not going to change, you should mail only if you really want to appear for examination and are unable to do so due to health reasons

~Sach Thadani