The problem ended up being related to the Apache reverse proxy rules that sit infront of Zimbra. Zimbra uses the following URL for accessing the user's mailbox items:
https://DOMAIN.COM/home/~/....
Apache did not have a reverse proxy rule to pass that URL on to Zimbra. The following directive fixed it:
ProxyPass /home
https://IP_ADDRESS/home
ReverseProxyPass /home
https://IP_ADDRESS/home
Restart apache and everything works well.