A Debian user has reported the following issue at the Debian bug tracker (http://bugs.debian.org/500148):
Zabbix agent (and possibly zabbix_server, but I havent checked this)
doesn't appear to be able to bind to multiple network interfaces.
It's either all (0.0.0.0) or just one.
I have tried using:
ListenIP=127.0.0.1 192.168.1.10 10.0.0.1
but with the latter try, it'll only bind to 10.0.0.1.