There is a problem with Live calendar publishing – it keeps asking for the Live ID password over and over.
This is not a problem on your end and republishing the calendar will not stop the password dialog.
There is something wrong with the publishing server or LiveID. Unfortunately, the only way to get rid of the annoying prompt (before its fixed) is to stop publishing. Right click on the calendar, choose publish and select the option to stop publishing (removes it from the server) or remove it in tools, accounts, published calendars tab. Wait a few days and try republishing.
Published December 22, 2009. Last updated on June 17, 2011.