We discovered that the CRM email bounce-backs were not being processed, resulting in a very full mailbox. Nick renamed the inbox, essentially cleaning out the mailbox, thinking that maybe the box was too full to process the messages properly. This appears to have fixed the problem. We will look into whether these are being cleaned out properly when the bounceback is processed (or, being marked for deletion but then never deleted).
We also discovered that messages were being routed to the Junk email mailbox. CRM only processes bounce-backs found in the Inbox. We suspect that our use of Outlook to access the bounces email account has caused this to occur. We will look into using a tool other than Outlook for accessing this IMAP account.