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Killing the perl processes helped me too. A simple 'zmlogswatchctl restart' didn't work; after going to the server status webpage, the service would die with the OP's error message.
$ ps auxwww|grep [/]zmlogger # list all zmlogger processes
$ ps auxwww|grep [/]zmlogger | awk '{ print $2; }' | xargs kill # kill all zmlogger processes
$ zmlogswatchctl restart # restart zmlogger
$ zmlogswatchctl status # get status