We take full backup of the db's daily and all of a sudden we start seeing this error for last 3 days for one particular db. Nothing has changed and there are other db's that are working fine.
That does not answer the questions I posed.
Try running RESTORE LABELONLY using the file name you are trying to back up to, e.g.
RESTORE LABELONLY FROM DISK = '<your file name>'
Firstly, does the file already exist? If it does, how many rows are returned, and what is the FamilyCount value? You can then find out the names of the files in that existing backup set using the following:
FROM msdb..backupmediaset a
INNER JOIN msdb..backupmediafamily b ON a.media_set_id = b.media_set_id
WHERE a.media_uuid = '<the MediaSetID value found in the backup set label>'
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