If there are are scripts running and the Zabbix agent somehow dies, simply starting it again won't work.
It then shows:

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15170:20110615:151448.782 Listener failed with error: zbx_tcp_listen() Fatal error: unable to serve on any address. [[(null)]:10050]
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After killing the userparameter scripts (ps aux | grep zabbix), the zabbix agent starts up just fine.
This has already happened a few times on different servers, so it looks like some kind of agent bug.