In the SQL Agent job the error was shown by
Executed as user: *****. sqlmaint.exe failed. [SQLSTATE 42000] (Error 22029). The step failed.
The Maintenance plan log said:
 Database ServicedeskDB: Database Backup...
[Microsoft SQL-DMO (ODBC SQLState: 42000)] Error 3202: [Microsoft][ODBC SQL Server Driver][SQL Server]Write on '********201103082203.BAK' failed, status = 112. See the SQL Server error log for more details.
[Microsoft][ODBC SQL Server Driver][SQL Server]BACKUP DATABASE is terminating abnormally.
In the SQL Error Log There were these entries.
2011-03-08 22:04:11.52 spid66 BackupMedium::ReportIoError: write failure on backup device '********201103082203.BAK'. Operating system error 112(error not found).
2011-03-08 22:04:11.53 spid66 Internal I/O request 0x6B514990: Op: Write, pBuffer: 0x06350000, Size: 983040, Position: 4470543872, UMS: Internal: 0x103, InternalHigh: 0x0, Offset: 0xA771600, OffsetHigh: 0x1, m_buf: 0x06350000, m_len: 983040, m_actualBytes: 0, m_errcode: 112, BackupFile: ********201103082203.BAK
2011-03-08 22:04:11.53 backup BACKUP failed to complete the command BACKUP DATABASE [*****] TO DISK = N'********201103082203.BAK' WITH INIT , NOUNLOAD , NOSKIP , STATS = 10, NOFORMAT
By the SQL Error Log it could look like a storage failure :-(
Not a nice way to start the day.
When I looked at the Windows System Log there were no entries on storage failure.
But looking at the storage I saw that there were 4.15 GB available, and that the last backup took 4.16 GB.
After a quick cleanup and a manual execution of the job - with success - the conclusion is that the error indicates a lack of available storage.