Why doesn't LiteSpeed append the backup file when the Backup Wizard selection is 'Append' (the default setting) and not selected 'Overwrite'?
During backup, if the user is naming the backup file, then LiteSpeed finds that existing backup file and appends it.
If the user is not naming the backup file, then by default, the existing backup file is not specified by name, LiteSpeed creates a unique file named with the database + date/time stamp D:\Backup\Northwind200609290527LiteSpeed_Full.BKP. If, on your next backup, you chose the previously created file named 'D:\BackupNorthwind200609290527LiteSpeed_Full.BKP', LiteSpeed would append to that file and no new file would be created.
For additional information, see: http://msdn2.microsoft.com/en-us/library/ms191505.aspx
All versions of SQL Server
All versions of LiteSpeed