I spent a lot of time trying to debug the following issue:

Suddenly we stopped receiving alerts in the dashboard for hosts in certain subnet (also in a separate Zabbix group, monitored by separate Zabbix proxy). The email notifications worked, though.
Initially I suspected that this was an issue on the proxy, even went so far as to recreate that proxy's DB. No luck. Spent half a day digging thru (other) performance problems with Zabbix, still looking for the mysterious bug. No luck again.
We've thought at the time the bug was affecting every trigger on the host, and couldn't find it.

At the end of a day I discovered by chance that the gateway for this host stopped responding to ICMP pings awhile ago, then I had a theory... It turned out that all of our hosts had a trigger for this host being unreachable, with expression like 'agent.ping.nodata(300). Also that trigger was dependent on a trigger for that hosts's gateway being unreachable. Strangely, when I had this linked to the "Host unreachable" trigger, the alerts for unreachable hosts stopped popping up on the dashboard if the gateway for this host didn't respond to ICMP pings, even if the "gateway unreachable" trigger itself was disabled.
But what's more strange, we kept receiving email alerts for those unreachable hosts.