This issue can be down to the user the Task Server is set to run as:
If the Task Scheduler job has Run with Highest Privileges ticked it will run as Administrator, if Outlook is not run this way there is a conflict and so won't have any communication from the task server.
You can test this:
Opening Outlook via right-clicking the shortcut and selecting Run as Administrator
If the emails then send then you know this has worked
If so, untick the option in Task Scheduler and run Outlook normally to make sure there are no accidental issues following a manual restart
How to check if Outlook and the Task server run with highest priviledges
Open Task manager
Go to the details tab
Right click on the columns
Press choose columns
Select "Elevated" Now check it the task servers and Outlook have both either Yes (meaning they run as admin/with highest priviledges) or No
If you have any further issues then please raise a new case online and reference the title of this article.