I know we have similar issues open but this one seems different than what I've seen before.
Start with a connection to a Jetpack site that is no longer online and which is getting notifications about the site being down.
Users should be able to disconnect a site
They can't select the site to disconnect it. Even if I try to go to https://wordpress.com/settings/general/sitename.com I get "Finishing Setup..." and flashing "Loading" sign on the left.
OSX/Chrome (Both current)

We frequently run across this in the forums:
http://en.forums.wordpress.com/topic/my-sites-doesnt-work
@ockham something to think about with the disconnect survey you are working on is whether folks can disconnect if their site is down to begin with :)
I started with a previously connected Jetpack site that is currently down. (It was a temporary site and I received a Jetpack Monitor notification when it went down.) The Jetpack debugger gave an unknown error, and this was the detailed connection error:
The Jetpack site is inaccessible or returned an error: Jetpack: [http_request_failed] cURL error 56: Recv failure: Connection reset by peer [-10520]
I followed these steps to disconnect the site:
Result: The site was successfully disconnected.
If some users are still getting the issue described in the original report, it would help to know more about the state of their site so we can investigate that specific case, as it doesn't seem to be an issue for all broken Jetpack sites.
Just adding to this issue, the same problem was encountered by a user (in 1230985-zen) whose site does not exist anymore, and as such the site did not show up under My Sites in order for them to be able to disconnect Jetpack.
They had been receiving repeated emails from Jetpack saying their site was down but couldn't seem to do anything about it.
This has been resolved now but is another example of confusion in the Jetpack disconnection flow (following the same steps to reproduce as explained by @supernovia ).