Steps to reproduce:

1. I set Linux by Zabbix agent template to ahost
2. I create a trigger action, based on Linux by Zabbix agent, and Zabbix agent is not available trigger. I set send messages to users. Set it enabled.
3. I stop the agent on the client host.
4.  

Result:

1. Wait 3 min, and I can see Zabbix agent is not available (for 3m) in the problems list, but e-mail has not sent.
2. When I set different trigger (for example has been restarted), it sends the e-mail alert.