Hello,
I just tested several scenarios with my tasks, went through the steps you describe in your original post twice and everything worked perfect for me.
The only problem I see is that when I change the Due Date inside Outlook the Time on the due date is reset to 12:00 AM on the new date but the new Due Date is reflected correctly. I can change the dates Online and on the tracked task in Outlook and the changes are going back and forth, never once my due date was wiped out.
Maybe we can try to find out what is the difference between a machine that produces a "colossal failure" and mine which works as designed.