I have exactly the same problem with Windows 7 x64 Ultimate and home. The only difference is that there are no errors or warnings to help identify the cause.

I use the Internet Security Suite 9.1.603.000, three PC license

The three affected machines are a new HP Pavillion laptop, old desktop with ASUS crosshair motherboard, new desktop with gigabyte GA-X58A-UD7.

Symptoms: PCs start ok and have network connectivity. After some time (anywhere from 60 seconds to an hour) the network drops out and the machine locks up - can not start or use explorer, iexplore or firefox.
"net use" reports that drives are reconnecting. It is not possible to disconnect the drives.
The machines can not be shutdown safely. You must hold down the power button or unplug it.

As this affects three completely different machines with different hardware and cpus my solution was to uninstall zonealarm and install an alternative firewall. It is obvious that there is an incompatibility between ZA and Windows 7