I have successfully implemented the VBA code from this link to download the attachment in each email to a folder:
Read more about that in the Turn on Cached Exchange Mode article.
As a possible workaround you may get access to online items in the folder if you consider using a low-level API on which Outlook was built. Or just consider using any third-party wrappers around this API such as Redemption.
EWS (or Graph API in case of Office 365) is also a possible solution, see Explore the EWS Managed API, EWS, and web services in Exchange for more information.