First thing I would do is see if you get the same delay in a un-customized Workspace. This will tell if there is something to look for in your customization or not. Also, the version and SP level you are using may be helpful to know.
Next, ensure you have the latest fixes for whichever SP you are on. Note that the workspace source provided in a patch/SP stays in the patch/SP folder, it doesn't overwrite the original install folder source, so make sure your customization is on the updated source.
My guess is that the task is being pushed the client (workspace) but isn't being shown, either due to your customization or on older source, because of a missing refresh. The tasklist is bound to a dataprovider from a LiveCycle DataService. But very hard to determine why the refresh isn't occuring.
Another way to prove if the task is making it to you customized workspace is to use the Charles Web Debugging Proxy product to trace your http session. It understands the AMF protocol used by Workspace and LiveCycle DataServices. Look in the workspace-server/messagebroker/amfpooling messages at the time you expect the task to be pushed down from the server and you should see the task in one of the responses.
Thank you for your reply.
My client is using LCES 8.2.1SP2 and they do not intend to upgrade to 8.2.1SP3. Next time they will upgrade to LCES 2.
They do not install default workspace.
I did not base on workspace source code to do the customized workspace, I use library workspace-runtime.swc instead. This swc library i extract from C:\Adobe\LiveCycle8.2\deploy\adobe-workspace-client.ear file, not from the default location C:\Adobe\LiveCycle8.2\LiveCycle_ES_SDK\misc\Process_Management\Workspace (which is 8.2 and never be updated after the patch).
I'm sure this is correct version of swc libary because previously we have a very hard time with SSO over SSL when I compile with default workspace-runtime swc file.
For the session, previously when i query available task for user in actionscript, i always trace out the task id. When the situation happens, from the flashlog.txt, i did not see the assigned task id until 2 - 5 mins later.
E.g. if from adminui, i see the task is assigned to user, and the task id is 135, when user go to the customized workspace, i cannot see the task id 135 in the trace log file, until 2 - 5 mins later.