Email sent to and Exchange online resource is being auto-deleted.

It's an option of the resource mailbox:

Set-CalendarProcessing roommailbox -DeleteNonCalendarItems $false

For more info refer to the cmdlet help: https://technet.microsoft.com/en-us/library/dd335046(v=exchg.160).aspx

In addition, you might want to check for rules, both Inbox and Transport ones.