After upgrading Debian, OpenDKIM sometimes stops running or fails to properly restart. If you don’t actively monitor your ZCS server, the only way to detect this is either through a growing mail queue of unsent messages or through a note in the ZCS server admin panel.
Usually, manually restarting either OpenDKIM itself or the whole ZCS server once “fixes” the problem:
# service zimbra restart
# /etc/init.d/zimbra restart
In other cases, fixing the permissions may help:
# /opt/zimbra/libexec/zmfixperms -verbose -extended