The Zabbix daemons should keep track of changes in resolv.conf. Changes to this file otherwise demand a restart of the daemon to become effective.
With a glibc default timeout of 5 seconds, name resolution might not work properly anymore – no matter if name resolution is set to round robin or not.
nscd uses inotify to keep track and it calls res_init() upon changes, as far as I saw. nsswitch.conf should probably also be taken care of.