When you send email messages to a mailbox in Microsoft Exchange Online, the messages aren't delivered, and you receive the following error message:
Remote Server returned '554 4.3.2 mailbox busy; STOREDRV.Deliver.Exception:StoragePermanentException.MapiExceptionMaxObjsExceeded; Failed to process message due to a permanent exception with message Cannot complete delivery-time processing.
This problem may occur if the mailbox has reached the limit of items in a folder. In Exchange Online, the limit is one million.
To resolve this problem, move emails from the folder that contains one million items to another folder or to an archive.