If you moved from Exchange servers, and did not re-run permissions wizard and Mailstore wizard, then you need to run these. Also, make sure Unity has access to the new Exchange store/server.. DNS is resolving correctly from Unity to new Exchange server, etc.
Chances are SQL isn't getting updated with the new MailstoreObjectID. You can look at the "Mailstore" table, and verify each mail store's MailstoreObjectID then compare the value to that of the subscriber's MailstoreObjectID that they belong to (or should belong to) which is located in the "Subscriber" table under MailstoreObjectID column.
One way you can resync these is to run X:\Commserver\ConfigurationSetup\setup.exe /sync
Or, for the ambitious customers (TAC doesn't recommend this), you can modify SQL for say, 1 user, to verify it gets pointed to the new mail store and test.
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...