I have a user who cannot archive deleted items to the standard Office 365 archive file. I've tried right clicking on deleted items, properties, clicking on auto archive, telling it to "Archive this folder using these settings: clean out items older than 3 months, move old items to default archive folder" and it still does not work.
I'm going to assume this is by design. I believe they were coming from a hosted Exchange or maybe IMAP previously so they'd clean out their PST files by quarters. I've re-created a new profile within Outlook and starting fresh to no avail.