While we wait for the publishing problems at Office Online to be fixed, try this workaround – it finally worked for me after several tries.
Go to office.com and sign in with the same Live ID you use to publish your calendar and select "Save my e-mail address and password". Restart Outlook and the browser. It should now work for either publishing or updating a subscribed calendar, at least until you sign out of Office Online and/or LiveID.
I’m not sure what the secret to making it work is – I trusted Microsoft.com for both web and cookies, set cookie handling to allow all cookies, restarted both Outlook and IE, and deleted saved passwords in Control Panel, User accounts.
Published December 29, 2009. Last updated on June 17, 2011.