This article talks about this limitation about Exchange online mailbox, however it doesn't contains the limitation about mailbox connection. So, I would suggest you open a service request to confirm with Office 365 team. They may could find some information for you.
Based on your description, I think there exist limitation about Exchange online mailbox connection, why not set up a scheduled task for backup at night? (Personally, Microsoft will ensure the continuous operation of Office 365, and there is no need for backup)
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