The scenario is using incoming email, an item is created in principal list which trigger principal workflow automatically. Then a task item is updated in the task list by the principal workflow. the workflow associated with the task list does not trigger. Both workflows'status was marked as completed and both of them run under system account. What is problem?
You will need to run workflows under user account not system account.
A workflow running under the system account cannot trigger a secondary workflow.
Have you tried explicitly calling the 2nd workflow from the 1st?
If you set the second workflow up as a 2010 workflow you should be able to call it at the end of the 1st workflow.