You should never rebuild an Identity with an Exchange account. If you have mail under "On My Computer" folders and Outlook will not open you might be forced to rebuild, but you should immediately delete the Exchange account and then add it back to let
the messages download from the server. If you damage the Exchange data and it uploads back to the server it's difficult to clean up.
I suggest you move to a new Identity. How to move your data to a new Identity
Exchange Basics
The Inbox syncs more frequently than any other and should be kept as clean as possible. (this is the number one cause of problems with sync).
Do NOT make subfolders under the Inbox.
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.
MORE INFO
Recommended Mailbox Size Limits
While you can stuff a folder with thousands of messages, you should keep folders under 2GB. Outlook uses the 2GB .mbox.