>I am trying to set up regular backups of transaction logs, but on one database the transaction log backup fails. When I go to the backup window to do it manually, the 'transaction log' and 'File and Filegroup' selections are grayed out and non-selectable. I have not been able to find any database setting that precludes transaction log backups, or any differences between databases that allow transaction log backups and the one that does not.

What's recovery model for the DB in question? The Transaction log backup is unavailable for the Simple recovery model. See BOL for details.