Hi Evan,
From your previous post, I understand that the user account may create many subfolders under inbox. I suggest please do not create subfolders under Inbox but at root level of Exchange.
Exchange Basics
The Inbox syncs more frequently than any other and should be kept as clean as possible.
Any folder with more than a few thousand messages is going to take some time to fully come down when you first sync your account. Due to the design of Outlook's sync engine (and how exchange works), you will see the 512 newest messages in a folder at the initial start of sync then the rest of the folder's contents will be back filled before you see any mail that arrives after this point. This is why it will look like you are not getting new mail when a folder is still going through initial sync. This is also further exacerbated by an Exchange issue where it gets unnecessary change events before the newer mail arrives. If you carefully watch the progress during the sync of a folder with greater than a couple thousand messages, you will see "Updating local..." a lot before the newer mail starts arriving (newer than the initial 512 that come down).
Outlook checks the server for updates every minute, any folder that has updates will subsequently be synced. Since Outlook has a limit on how many folders can be synced at a time, there can be a queue of folders waiting. The Inbox does get high priority so it will generally sync before other folders that also need to sync.
So I suggest you can recommend customer to clean up the subfolder, or for test purpose, you can let user configure a clean mailbox under the same problematic computer to see whether issue will persist to narrow down the root cause.
Regards,
Pinko