This actually affects 4.0.3, but I can't see any mention of it in a support ticket so I'm raising it in case it affects later versions

Last line in file zabbix_proxy.log.1:

zabbix_proxy [20999]: cannot open "/var/log/zabbix/zabbix_proxy.log": [13] Permission denied

The line before it is at 06:25 so I assume this was an artefact of log rotate. 

This happened randomly on a Sunday, and nobody had been on the machine. When I checked zabbix_proxy.log, it was owned by zabbix, but 0 bytes. 

All of the processes of the proxy were still running, but all idle. Because there is no trigger in Zabbix for when a proxy was last seen, it was only when I noticed that a host had no data that I started looking at this. The proxy had been stuck for several days by this point.