Zabbix server shows host available, though SNMP agent is down on remote host

[manu_dbpur]

I configured host in Agentless mode, i.e. with SNMPv3 only. Zabbix server could connect to host and show the data. But after some time, my SNMP agent on the monitered host went down, but Zabbix server is showing host is available in Hosts table and monitor status as monitered. I waited for almost 4 hrs and zabbix server is showing host is available.
I expected available status to be UNAVAILABLE in hosts table ?
Is this a bug in Zabbix ? or how do I configure zabbix to notify that the HOST is down in hosts window, when hosts snmp agent goes down.

[sbadger]

The host still shows up becasue the triggers still have data that is within the parameter. I had a simialr problem and then used the following trigger to let me know when I had a host that quite responding to snmp request:

{Host:sysUpTime.0.nodata(1200)}=1

This will set the trigger true if the parmater of sysUpTime gets no data changes for more than 1200 seconds. So far it has worked very well fo me.