Possible workarounds as below: 

Stop and change the Cleanup Task

What the weekly change is for, is to prevent the errors from showing up again, except once/week. Each time it runs, you should check to see if it ran successfully, and if not, stop it and delete it again. You'll need to continue doing this until a fix can be found.

If task is disabled instead of cleanup, then NO data will be purged, and the table will grow unexpectedly. Perform cleanup on weekly basis. If issue continues, running it manually or daily is recomended.

To help prevent the on demand clean up task from running change the cleanup options and set the maximum number of working database rows to 1 Million.

Manually Delete the Data

Note: Truncating these tables will cause all task history to be removed. If there is task history data that is needed, it must be retrieved before truncating the tables.

Delete data in the database by truncating the following task tables:

TaskInstanceResults
TaskInstances
TaskinstanceParents
TaskInstancesStarted
TaskInstanceStatus
TaskOutputPropertyValue

ie Use the following SQL command
Truncate table Taskinstances

Note that you may have to monitor the following tables and see if the exceed 200k rows. If they do, then you should truncate them as well.
TaskInstanceSummaries
TaskInstanceEvents
TaskInstanceChildEvents
TaskInstanceExecutionInfo
TaskInstanceJobNodes
TaskInstanceresultSummaries

You may have to stop the Altiris Object host and Dataloadeder services if you are having problems truncating the tables. 

• Find the Cleanup Task Data task, and find all run instances (not the one that says "Pending" under the Status), and stop them. About every minute, refresh this page until they all show a big red X.　

• At that point, delete the run instances. By this time, you'll notice that the logs are no longer filling with errors.

• Now, modify the schedule (the one that says pending) to run weekly instead of daily.

Run a Cleanup Script on Clients

Create a new run script task with the following syntax:

---------------------------------------------------------
REM Get the Altiris Agent install path
FOR /F "tokens=2*" %%A IN ('REG.EXE QUERY "HKLM\Software\Altiris\Altiris Agent" /V "installdir"') DO SET AgentDir=%%B
set tempbat=%temp%\AgentClean.bat"

REM Create temporary batch file to execute while the agent restarts
echo "%AgentDir%\aexagentutil" /stop > %tempbat%
echo rmdir "%AgentDir%\TaskManagement\cache" /s /q >> %tempbat%
echo rmdir "%AgentDir%\TaskManagement\status" /s /q >> %tempbat%
echo rmdir "%AgentDir%\TaskManagement\statusXml" /s /q >> %tempbat%
REM echo rmdir "%AgentDir%\TaskManagement\lti" /s /q >> %tempbat%      -- remove away this remark if you are running on a TS 7.1 and above
echo ping localhost -n 30 >> %tempbat%
echo "%AgentDir%\aexagentutil" /start >> %tempbat%
echo exit >> %tempbat%

REM Executes temporary batch file
start "" /MIN %tempbat%
---------------------------------------------------------

Now find the machines which are spamming the server using task results. To do this, first of all you have to find what results are frequenty sent to the NS by those client mahines. Run the following SQL query to see what Tasks have had data sent up to the server in the last 24 hours.

*Stop the service "Altiris Client Task Data Loader" and "Altiris Support Service".

*Stop all the running "Cleanup Task Data Daily" from Altiris Console>Settings>Notification Server>Task Settings>Cleanup Task Data.

*Run Cleanup task data manually with the attached SQL query.

*Run the stopped services "Altiris Client Task Data Loader" and "Altiris Support Service".

*Change the schedule time of the "Cleanup Task Data Daily" to few minutes later to re associated the task with the windows schedule.

By following these steps, the error might get reproduced when you run the services again as there is a regular check for the "taskinstances" table not to exceed 250000 rows causes an "On-Demand Cleanup Task Data". You have to stop it from the console, start the Cleanup Task Data from the console (right click > Start Now), if the error appears again just stop the running Cleanup Task Data, and re-run it when you see that it returned a value of success or fail, this should be performed until all of the failed Cleanup Task Data tasks disappear, and be sure that it can run without problem on its scheduled time.

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If Null values are found frequently under following query results, it will confirm that there is a problem
select max(i.name) as Name,TaskVersionGuid, count(*) As count from taskinstances ti
left join itemversions iv
on ti.TaskVersionguid = iv.Versionguid
left join item i
on iv.Itemguid = i.guid
join Taskinstanceresults tir
on tir.TaskInstanceGuid = ti.TaskInstanceGuid
where tir.endtime > getdate() -1
group by TaskVersionGuid
order by count DESC
-------------------------------------------------------

If the query results show that there is NULL value in their name, then it will confirm that it is likely to be problematic task. Please copy that TaskVersionGuid and put it in for the following Query

-------------------------------------------------------
declare @TaskVersionGuid uniqueidentifier
set @TaskVersionGuid='XXXXXX-XXXXXXXX-XXXXXXXX'

select max(vc.name) as Name, ResourceGuid, Count(*) as Count from TaskInstances ti
join vcomputer vc
on ti.ResourceGuid = vc.Guid
where ti.TaskVersionGuid = @TaskVersionGuid
group by ResourceGuid
order by count DESC
--------------------------------------------------------------

Run the above script on all affected machines.