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

or

ListenIP=127.0.0.1 192.168.1.10 10.0.0.1

or

ListenIP=127.0.0.1
ListenIP=192.168.1.10
ListenIP=10.0.0.1

but with the latter try, it'll only bind to 10.0.0.1.