We already know “Microsoft has its own impressively resilient processes for backing up Office 365 services.” MS employs the 3-2-1 backup rule; three copies of the data on two different media with one copy off-site. Microsoft does more than the minimum to cover itself.
From what I have read: Exchange Online Data is stored at data centers in Quicy, WA; Chicago, IL; San Antonio, TX; and Des Moines, IA. Microsoft allegedly stores data in at least two of the data centers for availability at all times. This is in addition to whatever processes they do not tell you publicly.
Now move the responsibility to yourself: The data is in the cloud, but what is YOUR second backup option? Relying soley on Microsoft to keep a copy of your data is only one media. And the files stored locally on your Outlook client are incomplete, because you have deleted email / files over time.
CLASS COMPUTING HAS EXCELLENT SOLUTIONS.
The Deleted Items Folder can have a retainage policy of: 14 Days, 30 Days, 60 Days, etc; this comes with limited functionality. Third-party solutions are more robust and easier to use. Class Computing has a complete back-up offering.