As part of the maintenance plan, the option to write to the sysdbmaintplan_history table is enabled so that the history can be logged. If the Litespeed logging is disabled then it populates the sysdbmaintplan_history table after a successful execution of the maintenance plan. If the litespeed logging is enabled then no data is populated within the sysdbmaintplan_history table, which means no history for backup jobs is recorded.
This problem only occurs on LiteSpeed versions prior to 4.5. The issue was a known bug where enabling the logging disabled the option for writing to the sysdbmaintplan_history table.
Issue has been fixed in release 4.5 and all subsequent releases. The latest release of LiteSpeed for SQL Server can be downloaded at: