For me, it was because the backup file was still open by another process. Here's the event log:
BackupDiskFile::OpenMedia: Backup device 'X:\Backups\MyDatabase\MyDatabase_backup_2014_08_22_132234_8270986.bak' failed to open. Operating system error 32(The process cannot access the file because it is being used by another process.).
Simply closing and reopening Sql Server Management Studio resolved it (so obviously it was ssms.exe that had the handle..)