Thanks for the suggestion, I tried it this afternoon. I found out that the "Taskbar Jump Lists" deletes the Quick Access file list.
It's not necessarily intuitive and the explanation on the Piriform page doesn't give much more clarification.
The relation I can find is when you right click on for instance the Excel icon, you see the most recent files at the top of the taskbar pop-up. This list is aggregated from all programs in Quick Access.