Similar problems can be found at:
https://www.zabbix.com/forum/showthread.php?t=45079
&&
https://www.zabbix.com/forum/showthread.php?t=49094

We use Debian 7 x64 VMs on VMware as Zabbix Proxys. We install the Zabbix components from the official repo, using the following guide:
https://www.zabbix.com/documentation/2.4/manual/installation/install_from_packages

The packages and the binarys itself work fine. The init scripts also work fine if you use them from the command line.

But if we have to reboot a VM, only the Proxy or the Agent are started. See the Forum posts for example.

What can i provide to help you solve that problem?